Coupled Anharmonic Oscillators. I. Equal-Mass Case
- 15 November 1973
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 8 (10), 3346-3366
- https://doi.org/10.1103/physrevd.8.3346
Abstract
This is the first in a series of papers on the large-order behavior of perturbation theory for coupled anharmonic oscillators. We exploit previously published dispersion techniques to convert the calculation of perturbation theory in large order into a barrier-penetration problem. We then introduce new semiclassical methods for describing tunneling through nonspherically symmetric, -dimensional potentials. To illustrate our new methods, we calculate the large-order behavior of perturbation theory for a simple system of two equal-mass oscillators with quartic coupling. Our predictions are in complete agreement with computer calculations. We then extend our results to oscillators with coupling, -oscillator systems, and some infinite-oscillator systems.
Keywords
This publication has 11 references indexed in Scilit:
- Anharmonic Oscillator. II. A Study of Perturbation Theory in Large OrderPhysical Review D, 1973
- Short-Distance Behavior of Quantum Electrodynamics and an Eigenvalue Condition forPhysical Review D, 1973
- Anharmonic Oscillator with Polynomial Self-InteractionJournal of Mathematical Physics, 1972
- Short-Distance Behavior of Quantum Electrodynamics and an Eigenvalue Condition forPhysical Review D, 1972
- Large-Order Behavior of Perturbation TheoryPhysical Review Letters, 1971
- Coupling constant analyticity for the anharmonic oscillatorAnnals of Physics, 1970
- Anharmonic OscillatorPhysical Review B, 1969
- Analytic Structure of Energy Levels in a Field-Theory ModelPhysical Review Letters, 1968
- Divergence of perturbation theory for bosonsCommunications in Mathematical Physics, 1965
- Divergence of Perturbation Theory in Quantum ElectrodynamicsPhysical Review B, 1952