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Annals of Physics

Operator Method in the Problem of Quantum Anharmonic Oscillator

И. Д. Феранчук, L I Komarov, I.V. Nichipor, Alexander P. Ulyanenkov

Published Mar 1, 1995• 57 citations
Publisher
DOI
10.1006/aphy.1995.1025

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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.