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Cite Details

Carl M. Bender and Luis M. A. Bettencourt, "Multiple-Scale Analysis of the Quantum Anharmonic Oscillator", Physical Review Letters, vol. 77, pp. 4114-4117, 1996


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.

BibTeX Entry

author = {Carl M. Bender and Luis M. A. Bettencourt},
title = {Multiple-Scale Analysis of the Quantum Anharmonic Oscillator},
year = {1996},
journal = {Physical Review Letters},
volume = {77},
pages = {4114-4117}