"Semiclassical Interpretation of Eigenvectors for Excited Atoms in Exte" by Robert Leonard Waterland, M. L. Du et al.
 

Document Type

Article

Department/Program

Physics

Journal Title

Physical Review A

Pub Date

2-1988

Publisher

American Physical Society

Volume

37

Issue

4

First Page

1185

Abstract

Eigenvectors for an electron in an atom in parallel electric and magnetic fields are calculated, and a semiclassical interpretation of their behavior is obtained. Eigenvectors can in this case be regarded as ‘‘wave functions in angular momentum space.’’ The matrix equation defining the eigenvectors is written as a difference equation, and then converted to a pseudodifferential equation; a systematic procedure is then used to construct a semiclassical approximation. It is found that the same classical Hamiltonian that has been previously used to calculate semiclassical eigenvalues provides a WKB-type representation of the eigenvectors. The development sheds new light on action-angle formulations of quantum mechanics and on semiclassical approximations in action-angle variables.

DOI

https://doi.org/10.1103/PhysRevA.37.1185

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