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 2nd 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI happened to have need for a stub _[[Born-Oppenheimer approximation]]_

   I happened to have need for a stub Born-Oppenheimer approximation

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJun 3rd 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI think that in the abstract form (at least in the generality I was doing research when working on a project in physical chemistry) Born-Oppenheimer approximation is about the distinction between fast changing and slow changing degrees of freedom; there is perturbation theory associated to the decomposition of the Hilbert space into products (that is we have a tensor product decomposition of the Hilbert space). The fact that the motion of heavy particles and light particles in a system is a special case of that is not essential for general statement of the problem. One has to write a general form of Hamiltonian which corresponds to the interpretation which makes plausible the perturbation theory in which the slowliness of some degrees of freedom is capitalized on. I do not have my notes with me, but I think it is not to difficult to recnstruct he general framework.

   I think that in the abstract form (at least in the generality I was doing research when working on a project in physical chemistry) Born-Oppenheimer approximation is about the distinction between fast changing and slow changing degrees of freedom; there is perturbation theory associated to the decomposition of the Hilbert space into products (that is we have a tensor product decomposition of the Hilbert space). The fact that the motion of heavy particles and light particles in a system is a special case of that is not essential for general statement of the problem. One has to write a general form of Hamiltonian which corresponds to the interpretation which makes plausible the perturbation theory in which the slowliness of some degrees of freedom is capitalized on. I do not have my notes with me, but I think it is not to difficult to recnstruct he general framework.