Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 10th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexin analogy to what I just did at [[classical mechanics]], I have now added some basic but central content to [[quantum mechanics]]: * Quantum mechanical systems * States and observables * Spaces of states * Flows and time evolution Still incomplete and rough. But I have to quit now.

   in analogy to what I just did at classical mechanics, I have now added some basic but central content to quantum mechanics:

   • Quantum mechanical systems

   • States and observables

   • Spaces of states

   • Flows and time evolution

   Still incomplete and rough. But I have to quit now.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2011
   • (edited Jun 12th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI like the idea section but I am surprised in generality and poor structure required in the main part (definition etc.). I mean one usually takes the Hilbert space, and C-star algebra. Now having only star algebra, which may be in principle of uncountable infinity of dimensions makes me hard to believe that everything makes sense. GNS construction in uncountable number of dimensions ? I know that some people have ideas of working in different topoi, but this needs various justification and is certainly not helpful for the casual user wanting to see the non-disputed basics. I think we should start with conventional case, where one has C-star algebra etc. and have special sections or entries for generalizations, which are many and in many direction.

   I like the idea section but I am surprised in generality and poor structure required in the main part (definition etc.). I mean one usually takes the Hilbert space, and C-star algebra. Now having only star algebra, which may be in principle of uncountable infinity of dimensions makes me hard to believe that everything makes sense. GNS construction in uncountable number of dimensions ? I know that some people have ideas of working in different topoi, but this needs various justification and is certainly not helpful for the casual user wanting to see the non-disputed basics.

   I think we should start with conventional case, where one has C-star algebra etc. and have special sections or entries for generalizations, which are many and in many direction.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI think it is good not to impose $C^*$-algebra structure in general. Many and most standard systems don't come with bounded operators, and one has to bend over backwards to make make them such.

   I think it is good not to impose $!A = \sum_{E: V} (E \to A}C^*$-algebra structure in general. Many and most standard systems don’t come with bounded operators, and one has to bend over backwards to make make them such.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2011
   • (edited Jun 12th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt is not easy to remove the C-star algebra. For example, what about he GNS construction I asked above ? Inner product in non-separable case ? How about KMS state and time evolution ? Some topological or categorical restrains are needed to make things contentful: some sort of spectral theory is needed to make sense of observables and measurement. Unbounded operators can be dealt in many ways, for example by looking at the associated multiplier algebra of the C-star algebra. One can also look at $W^*$-algebras. But, alternatively, dispensing with the spectral theory of Banach algebras or alike is really problematic. To talk about quantum mechanics it is not sufficient to have some abstract algebra, one has to make sense of measurement.

   It is not easy to remove the C-star algebra. For example, what about he GNS construction I asked above ? Inner product in non-separable case ? How about KMS state and time evolution ? Some topological or categorical restrains are needed to make things contentful: some sort of spectral theory is needed to make sense of observables and measurement. Unbounded operators can be dealt in many ways, for example by looking at the associated multiplier algebra of the C-star algebra. One can also look at $W^*$-algebras. But, alternatively, dispensing with the spectral theory of Banach algebras or alike is really problematic. To talk about quantum mechanics it is not sufficient to have some abstract algebra, one has to make sense of measurement.

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2011
   • (edited Jun 12th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThere is another thing which I see as a problem with the entry. The claim that one dimensional quantum mechanics is a Riemannian 0+1-dimensional field theory. So let me take an arbitrary example from textbooks of a space in k-dimensions $x_1,\ldots, x_n$ and a time-dependent potential $V(x_1,\ldots,x_n,t)$. Now the formalism of quantization described first has slight problem with time-dependent Hamiltonian (that is fixable by having more general form of the evolution operator) but the problem is that the potential is not something what the category of Riemannian manifolds knows of. It knows of differentiable manifold and a metric on it. So how do you put the arbitrary potential on a specific space into the data of a category ? This is nothing unusual, most exercises in QM courses will have such a specific potential. As long as one has the Hamiltonian depending only on Riemannian structure I have no problem with the approach. But I do not see how to put the Hamiltonians which depend on the data which is not in the category. Say, you have a Coulomb potential in 3 dimensions for a time-independent case. What do you do to the category of Riemannian manifolds to produce a functor whose data are equivalent to the QM of such a Coulomb system in 3-dimensions ? Edit: it makes me very suspicious that it is possible to say, on the basis of what happens in one particular space with potential, what should functor do on all possible manifolds. Of course, one could consider ALL spaces with all potentials and put them somehow into the category, but this is cheating, as it does not distinguish different quantum mechanical systems (i.e.different potentials) as phrased in the usual way. I would say that a quantum field theory in 0+1-dimension is a general prescription on how to use the type of geometric data as an input for evolution operators (with worse case in the case of time-dependent potentials). This way diverging theories which do not make sense from the usual perspective and the converging theories which do are parts of the data of the same "field theory". Of course if no potential than there are field theories whose all instances (that is for all input spaces) are equally OK from the usual formalism.

   There is another thing which I see as a problem with the entry. The claim that one dimensional quantum mechanics is a Riemannian 0+1-dimensional field theory. So let me take an arbitrary example from textbooks of a space in k-dimensions $x_1,\ldots, x_n$ and a time-dependent potential $V(x_1,\ldots,x_n,t)$. Now the formalism of quantization described first has slight problem with time-dependent Hamiltonian (that is fixable by having more general form of the evolution operator) but the problem is that the potential is not something what the category of Riemannian manifolds knows of. It knows of differentiable manifold and a metric on it. So how do you put the arbitrary potential on a specific space into the data of a category ? This is nothing unusual, most exercises in QM courses will have such a specific potential. As long as one has the Hamiltonian depending only on Riemannian structure I have no problem with the approach. But I do not see how to put the Hamiltonians which depend on the data which is not in the category. Say, you have a Coulomb potential in 3 dimensions for a time-independent case. What do you do to the category of Riemannian manifolds to produce a functor whose data are equivalent to the QM of such a Coulomb system in 3-dimensions ?

   Edit: it makes me very suspicious that it is possible to say, on the basis of what happens in one particular space with potential, what should functor do on all possible manifolds. Of course, one could consider ALL spaces with all potentials and put them somehow into the category, but this is cheating, as it does not distinguish different quantum mechanical systems (i.e.different potentials) as phrased in the usual way. I would say that a quantum field theory in 0+1-dimension is a general prescription on how to use the type of geometric data as an input for evolution operators (with worse case in the case of time-dependent potentials). This way diverging theories which do not make sense from the usual perspective and the converging theories which do are parts of the data of the same “field theory”. Of course if no potential than there are field theories whose all instances (that is for all input spaces) are equally OK from the usual formalism.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexFor time-dependent Hamiltonians (with whatever potential) one considers cobordisms with a map to a time-parameter space. Equivalently one can just mordify the cobordism category by having the objects be labeled in $\mathbb{R}$ and a cobordism of length $\ell$ go from object $t$ to object $t + \ell$.

   For time-dependent Hamiltonians (with whatever potential) one considers cobordisms with a map to a time-parameter space. Equivalently one can just mordify the cobordism category by having the objects be labeled in $\mathbb{R}$ and a cobordism of length $\ell$ go from object $t$ to object $t + \ell$.

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThanks for your approach to time-dependence: this was as I mentioned less serious objection (I propose above another remedy), the more serious is the correspondence for arbitrary potentials. I was thinking about this for lonmg time, asked about very many times before and every time I get such a neglecting response. Don't you see that this is one of the most important points of misunderstanding ??

   Thanks for your approach to time-dependence: this was as I mentioned less serious objection (I propose above another remedy), the more serious is the correspondence for arbitrary potentials. I was thinking about this for lonmg time, asked about very many times before and every time I get such a neglecting response. Don’t you see that this is one of the most important points of misunderstanding ??

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJun 12th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItex> asked about very many times before and every time I get such a neglecting response. Sorry, I don't know what this refers to. > Don't you see that this is one of the most important points of misunderstanding ?? I am not following. What is a point of misunderstanding?

   asked about very many times before and every time I get such a neglecting response.

   Sorry, I don’t know what this refers to.

   Don’t you see that this is one of the most important points of misunderstanding ??

   I am not following. What is a point of misunderstanding?

9. • CommentRowNumber9.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt refers to **potentials**. E.g. to the earlier extensive discussion on the difference between QM and QFT. I claimed that QFT is special case of QM and you that it is also true the opposite; and never got answered the main problem of your point of view about the inclusion of the space-dependent potential of a particular QM system. I can get the latter by a very unsatisfactory way, as mentioned above, to put all the possible space potentials on all possible Riemannian spaces simultaneously in the same category. This would mean a FQFT equivalent to all space potential QM systems at the same time. When you have TQFT then you distinguish different TQFTs, so one should also distinguish square well potential system from say Coulomb potential system in 3 dimension. The latter notions are not local notions but global in a sense. I understand that your point is to use the evolution operator as the part of a functor and every QM system has an evolution operator (in particular, every 4d AQFT also has an evolution operator and belongs to the same framework). But how do you distinguish different quantum mechanical systems. You have to take a different law of motion, different Hamiltonian, different evolution operator. But this operator is fed by the data in the underlying category. So if the underlying category is the category of Riemannian spaces, then I can take any polynomial scalar expression in terms of metrics and use it for Hamiltonian. Good, this is majority of examples in $n$Lab. Happy so far. But the potential is arbitrary, it does not take the metrics inside, it is just a function on the space. So the only way to take it is to put the function into the data. But I can hardly imagine a category of such, unless I put all possible potentials on all spaces in a category. But this is not the original QM system, this is the category of ALL QM systems of that type simultaneously. So the FQFT did not define a **particular** such system. FQFT defines all systems of the same structure type. Free fermionic theory for example. This is all possible free theories on all spaces. But Coulomb theory, well such a thing does not exist in FQFT world. Unless I misunderstand your point.

   It refers to potentials.

   E.g. to the earlier extensive discussion on the difference between QM and QFT. I claimed that QFT is special case of QM and you that it is also true the opposite; and never got answered the main problem of your point of view about the inclusion of the space-dependent potential of a particular QM system. I can get the latter by a very unsatisfactory way, as mentioned above, to put all the possible space potentials on all possible Riemannian spaces simultaneously in the same category. This would mean a FQFT equivalent to all space potential QM systems at the same time. When you have TQFT then you distinguish different TQFTs, so one should also distinguish square well potential system from say Coulomb potential system in 3 dimension. The latter notions are not local notions but global in a sense. I understand that your point is to use the evolution operator as the part of a functor and every QM system has an evolution operator (in particular, every 4d AQFT also has an evolution operator and belongs to the same framework). But how do you distinguish different quantum mechanical systems. You have to take a different law of motion, different Hamiltonian, different evolution operator. But this operator is fed by the data in the underlying category. So if the underlying category is the category of Riemannian spaces, then I can take any polynomial scalar expression in terms of metrics and use it for Hamiltonian. Good, this is majority of examples in $n$Lab. Happy so far. But the potential is arbitrary, it does not take the metrics inside, it is just a function on the space. So the only way to take it is to put the function into the data. But I can hardly imagine a category of such, unless I put all possible potentials on all spaces in a category. But this is not the original QM system, this is the category of ALL QM systems of that type simultaneously. So the FQFT did not define a particular such system. FQFT defines all systems of the same structure type. Free fermionic theory for example. This is all possible free theories on all spaces. But Coulomb theory, well such a thing does not exist in FQFT world. Unless I misunderstand your point.

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2011
    • PermaLink
    Author: Urs
    Format: MarkdownItexIt seems we have clarified this by private email now.

    It seems we have clarified this by private email now.

11. • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeJun 13th 2011
    • (edited Jun 13th 2011)
    • PermaLink
    Author: zskoda
    Format: MarkdownItexYes. I see your point. Remark: The same prescription knowing at object level only of a Hilbert space (and not of underlying geoemtric space, what was my misconception of the translation in 0-dimensional case), this prescription keeping only Hilbert space data could also make any AQFT in any number of dimensions a 0+1-dimensional FQFT (this is in agreement that AQFT may be viewed a special case of QM). The fact that FQFT wants to keep (in another prescription like your AQFT vs FQFT article) the same dimension for traditional QFT is just a preference of the formalism to keep features of the underlying space which intentionally lost in QM case. I understand your point that you keep the dimension of evolutions multiple for QFT, in the FQFT convention. Thanks.

    Yes. I see your point.

    Remark: The same prescription knowing at object level only of a Hilbert space (and not of underlying geoemtric space, what was my misconception of the translation in 0-dimensional case), this prescription keeping only Hilbert space data could also make any AQFT in any number of dimensions a 0+1-dimensional FQFT (this is in agreement that AQFT may be viewed a special case of QM). The fact that FQFT wants to keep (in another prescription like your AQFT vs FQFT article) the same dimension for traditional QFT is just a preference of the formalism to keep features of the underlying space which intentionally lost in QM case. I understand your point that you keep the dimension of evolutions multiple for QFT, in the FQFT convention. Thanks.

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2011
    • (edited Jul 9th 2011)
    • PermaLink
    Author: Urs
    Format: MarkdownItexI have added to [[quantum mechanics]] in the section "quantum systems" a subsection [quantum subsystems](http://ncatlab.org/nlab/show/quantum+mechanics#Subsystems) with two basic definitions.

    I have added to quantum mechanics in the section “quantum systems” a subsection quantum subsystems with two basic definitions.

13. • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeFeb 1st 2020
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded full publication data and hyperlinks to * [[Klaas Landsman]], _Foundations of quantum theory -- From classical concepts to Operator algebras_, Springer Open 2017 ([doi:10.1007/978-3-319-51777-3](https://link.springer.com/book/10.1007/978-3-319-51777-3), [pdf](https://link.springer.com/content/pdf/10.1007%2F978-3-319-51777-3.pdf)) <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/68">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/68">v68</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added full publication data and hyperlinks to

    • Klaas Landsman, Foundations of quantum theory – From classical concepts to Operator algebras, Springer Open 2017 (doi:10.1007/978-3-319-51777-3, pdf)

    diff, v68, current

14. • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to some of the historical articles: * [[Werner Heisenberg]], *Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen*, Zeitschrift für Physik **33** (1925) 879–893 $[$[doi:10.1007/BF01328377]( https://doi.org/10.1007/BF01328377), [Engl. pdf](http://users.mat.unimi.it/users/galgani/arch/heis25ajp.pdf)$]$ * [[Erwin Schrödinger]], *Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen*, Annalen der Physil **384** 8 (1926) 734-756 $[$[doi:10.1002/andp.19263840804]( https://doi.org/10.1002/andp.19263840804)$]$ * [[Paul A. M. Dirac]], *On the theory of quantum mechanics*, Proceedings of the Royal Society **112** 762 (1926) $[$[doi:10.1098/rspa.1926.0133](https://doi.org/10.1098/rspa.1926.0133)$]$ <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/72">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/72">v72</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to some of the historical articles:

    • Werner Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Zeitschrift für Physik 33 (1925) 879–893 $[$doi:10.1007/BF01328377, Engl. pdf$]$

    • Erwin Schrödinger, Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen, Annalen der Physil 384 8 (1926) 734-756 $[$doi:10.1002/andp.19263840804$]$

    • Paul A. M. Dirac, On the theory of quantum mechanics, Proceedings of the Royal Society 112 762 (1926) $[$doi:10.1098/rspa.1926.0133$]$

    diff, v72, current

15. • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJul 8th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded one more historical article: * [[Max Born]], [[Pascual Jordan]], *Zur Quantenmechanik*, Zeitschrift für Physik **34** (1925) 858–888 &lbrack;[doi:10.1007/BF01328531](https://doi.org/10.1007/BF01328531)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/73">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/73">v73</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added one more historical article:

    • Max Born, Pascual Jordan, Zur Quantenmechanik, Zeitschrift für Physik 34 (1925) 858–888 [doi:10.1007/BF01328531]

    diff, v73, current

16. • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeSep 29th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexI have added more publication data for: * [[John von Neumann]], *Mathematische Grundlagen der Quantenmechanik* (German) (1932, 1971) &lbrack;[doi:10.1007/978-3-642-96048-2](https://link.springer.com/book/10.1007/978-3-642-96048-2)&rbrack; *Mathematical Foundations of Quantum Mechanics* Princeton University Press (1955) &lbrack;[doi:10.1515/9781400889921](https://doi.org/10.1515/9781400889921), [Wikipedia entry](https://en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/79">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/79">v79</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    I have added more publication data for:

    • John von Neumann, Mathematische Grundlagen der Quantenmechanik (German) (1932, 1971) [doi:10.1007/978-3-642-96048-2]

      Mathematical Foundations of Quantum Mechanics Princeton University Press (1955) [doi:10.1515/9781400889921, Wikipedia entry]

    diff, v79, current

17. • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeOct 17th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[David Hilbert]], [[John von Neumann]], [[Lothar W. Nordheim]], *Über die Grundlagen der Quantenmechanik*, Math. Ann. **98** (1928) 1–30 &lbrack;[doi:10.1007/BF01451579](https://doi.org/10.1007/BF01451579)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/80">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/80">v80</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • David Hilbert, John von Neumann, Lothar W. Nordheim, Über die Grundlagen der Quantenmechanik, Math. Ann. 98 (1928) 1–30 [doi:10.1007/BF01451579]

    diff, v80, current

18. • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Serge Haroche]], [[Jean-Michel Raimond]], *Exploring the Quantum: Atoms, Cavities, and Photons*, Oxford University Press (2006) &lbrack;[doi:10.1093/acprof:oso/9780198509141.001.0001](https://doi.org/10.1093/acprof:oso/9780198509141.001.0001)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/85">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/85">v85</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Serge Haroche, Jean-Michel Raimond, Exploring the Quantum: Atoms, Cavities, and Photons, Oxford University Press (2006) [doi:10.1093/acprof:oso/9780198509141.001.0001]

    diff, v85, current

19. • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2022
    • (edited Nov 19th 2022)
    • PermaLink
    Author: Urs
    Format: MarkdownItexI have added pointer to: * [[Karl Kraus]], *States, Effects, and Operations -- Fundamental Notions of Quantum Theory*, Lecture Notes in Physics **190** Springer (1983) &lbrack;[doi:10.1007/3-540-12732-1](https://doi.org/10.1007/3-540-12732-1)&rbrack; While doing so, i have slightly re-arranged the list of textbooks under *[References -- General](https://ncatlab.org/nlab/show/quantum+mechanics#ReferencesGeneral)* in order to retain chronological and logical order. <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/87">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/87">v87</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    I have added pointer to:

    • Karl Kraus, States, Effects, and Operations – Fundamental Notions of Quantum Theory, Lecture Notes in Physics 190 Springer (1983) [doi:10.1007/3-540-12732-1]

    While doing so, i have slightly re-arranged the list of textbooks under References – General in order to retain chronological and logical order.

    diff, v87, current

20. • CommentRowNumber20.
    • CommentAuthorUrs
    • CommentTimeNov 25th 2022
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Stéphane Attal]], *Quantum Mechanics*, Lecture 5 in: *Lectures on Quantum Noises* &lbrack;[pdf](http://math.univ-lyon1.fr/~attal/Quantum_Mechanics.pdf), [webpage](http://math.univ-lyon1.fr/~attal/chapters.html)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/88">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/88">v88</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Stéphane Attal, Quantum Mechanics, Lecture 5 in: Lectures on Quantum Noises [pdf, webpage]

    diff, v88, current

21. • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Ingemar Bengtsson]], [[Karol Życzkowski]], *Geometry of Quantum States --- An Introduction to Quantum Entanglement*, Cambridge University Press (2006) &lbrack;[doi:10.1017/CBO9780511535048](https://doi.org/10.1017/CBO9780511535048)&rbrack; and will add this to a few related entries, too (such as to [[quantum state]], [[quantum entanglement]], ...) <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/90">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/90">v90</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Ingemar Bengtsson, Karol Życzkowski, Geometry of Quantum States — An Introduction to Quantum Entanglement, Cambridge University Press (2006) [doi:10.1017/CBO9780511535048]

    and will add this to a few related entries, too (such as to quantum state, quantum entanglement, …)

    diff, v90, current

22. • CommentRowNumber22.
    • CommentAuthorUrs
    • CommentTimeJul 3rd 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Robert Geroch]], *Geometrical Quantum Mechanics*, University of Chicago (1974) &lbrack;[pdf](http://strangebeautiful.com/other-texts/geroch-geom-qm.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/93">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/93">v93</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Robert Geroch, Geometrical Quantum Mechanics, University of Chicago (1974) [pdf]

    diff, v93, current

23. • CommentRowNumber23.
    • CommentAuthornLab edit announcer
    • CommentTimeJul 10th 2023
    • PermaLink
    Author: nLab edit announcer
    Format: MarkdownItexadding textbook * [[Peter Woit]], *Quantum Theory, Groups and Representations: An Introduction*, Springer 2017 &lbrack;[doi:10.1007/978-3-319-64612-1](https://doi.org/10.1007/978-3-319-64612-1), ISBN:978-3-319-64610-7&rbrack; Quinn <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/96">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/96">v96</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    adding textbook

    • Peter Woit, Quantum Theory, Groups and Representations: An Introduction, Springer 2017 [doi:10.1007/978-3-319-64612-1, ISBN:978-3-319-64610-7]

    Quinn

    diff, v96, current

24. • CommentRowNumber24.
    • CommentAuthorUrs
    • CommentTimeSep 11th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded more textbook pointers: * [[Jun John Sakurai]], Jim Napolitano, Cambridge University Press (1985, 2020) &lbrack;[doi:10.1017/9781108587280](https://doi.org/10.1017/9781108587280), [Wikipedia](https://en.wikipedia.org/wiki/Modern_Quantum_Mechanics)&rbrack; * [[Steven Weinberg]], *Lectures on Quantum Mechanics*, Cambridge University Press (2015) &lbrack;[doi:10.1017/CBO9781316276105](https://doi.org/10.1017/CBO9781316276105)&rbrack; * [[Chris Isham]], *Lectures on Quantum Theory -- Mathematical and Structural Foundations*, World Scientific (1995) &lbrack;[doi:10.1142/p001](https://doi.org/10.1142/p001), [ark:/13960/t4xh7cs99](https://archive.org/details/lecturesonquantu0000isha)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/104">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/104">v104</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added more textbook pointers:

    • Jun John Sakurai, Jim Napolitano, Cambridge University Press (1985, 2020) [doi:10.1017/9781108587280, Wikipedia]

    • Steven Weinberg, Lectures on Quantum Mechanics, Cambridge University Press (2015) [doi:10.1017/CBO9781316276105]

    • Chris Isham, Lectures on Quantum Theory – Mathematical and Structural Foundations, World Scientific (1995) [doi:10.1142/p001, ark:/13960/t4xh7cs99]

    diff, v104, current

25. • CommentRowNumber25.
    • CommentAuthorzskoda
    • CommentTimeSep 12th 2023
    • PermaLink
    Author: zskoda
    Format: MarkdownItexLink * Uni Bonn, _[Lecture scripts and Online courses -- Quantum mechanics](http://www-cip.physik.uni-bonn.de/~baehren/scripts/quantum.html)_ seem to be broken. I could not find a replacement link.

    Link

    • Uni Bonn, Lecture scripts and Online courses – Quantum mechanics

    seem to be broken. I could not find a replacement link.

26. • CommentRowNumber26.
    • CommentAuthorUrs
    • CommentTimeSep 12th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItex> I could not find... Of course [archive.org](https://archive.org/web) has the page ([here](https://web.archive.org/web/20001101031920/http://www-cip.physik.uni-bonn.de/~baehren/scripts/quantum.html)) <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/106">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/106">v106</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    I could not find…

    Of course archive.org has the page

    (here)

    diff, v106, current

27. • CommentRowNumber27.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Paul Busch]], [[Marian Grabowski]], [[Pekka J. Lahti]], *Operational Quantum Physics*, Lecture Notes in Physics Monographs **31**, Springer (1995) &lbrack;[doi:10.1007/978-3-540-49239-9](https://doi.org/10.1007/978-3-540-49239-9)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/108">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/108">v108</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Paul Busch, Marian Grabowski, Pekka J. Lahti, Operational Quantum Physics, Lecture Notes in Physics Monographs 31, Springer (1995) [doi:10.1007/978-3-540-49239-9]

    diff, v108, current

28. • CommentRowNumber28.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexand this one: * [[Teiko Heinosaari]], [[Mário Ziman]], *The Mathematical Language of Quantum Theory -- From Uncertainty to Entanglement*, Cambridge University Press (2011) &lbrack;[doi:10.1017/CBO9781139031103]( https://doi.org/10.1017/CBO9781139031103)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/108">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/108">v108</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    and this one:

    • Teiko Heinosaari, Mário Ziman, The Mathematical Language of Quantum Theory – From Uncertainty to Entanglement, Cambridge University Press (2011) [doi:10.1017/CBO9781139031103]

    diff, v108, current

29. • CommentRowNumber29.
    • CommentAuthorUrs
    • CommentTimeSep 23rd 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Robert B. Griffiths]], *Consistent Quantum Theory*, Cambridge University Press (2002) &lbrack;[doi:10.1017/CBO9780511606052](https://doi.org/10.1017/CBO9780511606052), [webpage](https://quantum.phys.cmu.edu/CQT)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/109">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/109">v109</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Robert B. Griffiths, Consistent Quantum Theory, Cambridge University Press (2002) [doi:10.1017/CBO9780511606052, webpage]

    diff, v109, current

30. • CommentRowNumber30.
    • CommentAuthornLab edit announcer
    • CommentTimeMar 5th 2024
    • PermaLink
    Author: nLab edit announcer
    Format: MarkdownItexChanging an link to an error page to a link to a working site (https://quantumpositioned.com/learn-quantum-mechanics/) Harry Hannan <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/116">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/116">v116</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    Changing an link to an error page to a link to a working site (https://quantumpositioned.com/learn-quantum-mechanics/)

    Harry Hannan

    diff, v116, current

31. • CommentRowNumber31.
    • CommentAuthorUrs
    • CommentTimeMar 5th 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexI have deleted the ambient paragraph "quantum physics in general", which was incoherent and didn't serve a good purpose. (Some text with that title might still be worthwhile, though.) In particular, this paragraph was clearly the wrong place to tacitly link to a site for learning quantum mechanics. <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/117">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/117">v117</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    I have deleted the ambient paragraph “quantum physics in general”, which was incoherent and didn’t serve a good purpose. (Some text with that title might still be worthwhile, though.)

    In particular, this paragraph was clearly the wrong place to tacitly link to a site for learning quantum mechanics.

    diff, v117, current

32. • CommentRowNumber32.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * Von Neumann's 1927 Trilogy on the Foundations of Quantum Mechanics (annotated translations by Anthony Duncan) &lbrack;[arXiv:2406.02149](https://arxiv.org/abs/2406.02149)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/quantum+mechanics/118">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+mechanics/118">v118</a>, <a href="https://ncatlab.org/nlab/show/quantum+mechanics">current</a>

    added pointer to:

    • Von Neumann’s 1927 Trilogy on the Foundations of Quantum Mechanics (annotated translations by Anthony Duncan) [arXiv:2406.02149]

    diff, v118, current