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I moved the following text here from the article page. I don't think it is helpful as it is, but it might save as a basis for phrasing a more accessible example.
In
classical mechanics (CM), at the molecular level, one can define a
potential energy surface. This is a purely classical construct and does not hold for
QM. In QM an
adiabatic state (i.e. not resonant with other states) will remain occupied. For example in a
diatomic, the classical interpretation of the stretch mode is a periodic
vibration. Here CM agrees with QM and the system is perfectly adiabatic (all the energy remains in the vib mode). On multidimensional surfaces one can imagine a surface where a
trajectory (i.e. a marble rolling on a surface w/o
angular momentum) might have an almost
periodic motion but just does not come back to exactly the same
phase space location (i.e. after one vibrational phase the
geometry and momenta of the
atoms of the
molecule are very similar but not exactly the same).
References:
This is a “Vague tori” as I understand it from Hase JPC 2009 jp806659f
This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of
Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.PhysicsWikipedia:WikiProject PhysicsTemplate:WikiProject Physicsphysics articles
I moved the following text here from the article page. I don't think it is helpful as it is, but it might save as a basis for phrasing a more accessible example.
In
classical mechanics (CM), at the molecular level, one can define a
potential energy surface. This is a purely classical construct and does not hold for
QM. In QM an
adiabatic state (i.e. not resonant with other states) will remain occupied. For example in a
diatomic, the classical interpretation of the stretch mode is a periodic
vibration. Here CM agrees with QM and the system is perfectly adiabatic (all the energy remains in the vib mode). On multidimensional surfaces one can imagine a surface where a
trajectory (i.e. a marble rolling on a surface w/o
angular momentum) might have an almost
periodic motion but just does not come back to exactly the same
phase space location (i.e. after one vibrational phase the
geometry and momenta of the
atoms of the
molecule are very similar but not exactly the same).
References:
This is a “Vague tori” as I understand it from Hase JPC 2009 jp806659f