## Abstract

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 language | English (US) |
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Pages (from-to) | 3366-3378 |

Number of pages | 13 |

Journal | Physical Review D |

Volume | 8 |

Issue number | 10 |

DOIs | |

State | Published - 1973 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)