Exact wave functions from classical orbits. II. The Coulomb, Morse, Rosen-Morse, and Eckart systems

Kenneth G. Kay

Research output: Contribution to journalArticlepeer-review

Abstract

Wave functions for the Coulomb, Morse, Rosen-Morse, and Eckart systems are expressed exactly and explicitly in terms of the corresponding classical trajectories. This is accomplished by a technique that maps previously obtained classical representations for wave functions of the three-dimensional isotropic harmonic oscillator to the wave functions for the present systems. By design, the classical behavior enters these expressions in a manner that allows them to be used as uniform semiclassical approximations for other systems. The construction of a hydrogen orbital from the corresponding classical orbits is illustrated for a particular case. The classical representation of the Eckart wave function is analyzed to understand how ordinary, real, classical trajectories that are confined to one side of a barrier are able to describe tunneling through the barrier.

Original languageEnglish
Pages (from-to)23
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume65
Issue number3
DOIs
StatePublished - 2002

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