Coupled anharmonic oscillators. II. Unequal-mass case

Thomas Banks, Carl M. Bender

Research output: Contribution to journalArticlepeer-review

157 Scopus citations


We develop a general formalism for calculating the large-order behavior of perturbation theory for quantized systems of unequal-mass coupled anharmonic oscillators. Our technique is based on a generalization of the semiclassical approximation which was used to study equal-mass oscillators in the first paper of this series. The unequal-mass problem is much more difficult because the path which minimizes the classical action is not a straight line. Assuming that this tunneling path is known, we derive a general expression for the physical-optics approximation to the wave function of a tunneling particle. This derivation rests on the construction of a WKB approximation in curved space. We thus completely reduce the general quantum problem to the much simpler classical one of determining the path. Then we present a perturbation scheme for finding the classical path for systems of oscillators whose masses only differ by a small amount. Finally, we illustrate our techniques by solving a two-mode unequal-mass oscillator and comparing these results with a computer calculation. Our theoretical predictions and numerical calculations agree.

Original languageEnglish (US)
Pages (from-to)3366-3378
Number of pages13
JournalPhysical Review D
Issue number10
StatePublished - 1973
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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