Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Carl M. Bender, Luís M. A. Bettencourt
Conventional weak-coupling perturbation theory suffers from problems that arise from the resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.
arXiv:hep-th/9605181•Physical Review Letters•Nov 11, 1996•85 citations