ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A fairly complete perturbation theoretical solution of the Schrödinger equation around a classical periodic orbit is given as an example demonstrating the quantization of a system with many degrees of freedom by the method of collective coordinates. In particular, explicit expressions are derived for the creation and annihilation operators of quantum fluctuations orthogonal to the classical path, as well as the corresponding eigenfunctions, in both the adiabatic and nonadiabatic domains. It is also shown that corresponding expressions become proportional (and thus can be linked) in domains where they overlap. Finally the splitting of asymptotically degenerate states, and hence the band structure of the resulting spectrum, is calculated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.526961
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