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Semiclassical Interpretation of Eigenvectors for Excited Atoms in External Fields
Waterland, Robert Leonard Du, M. L. Delos, John B
Waterland, Robert Leonard
Du, M. L.
Delos, John B
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.
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1988-02-01
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American Physical Society
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Physics
DOI
https://doi.org/10.1103/PhysRevA.37.1185