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arXiv · hep-th/9605181

Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

Carl M. Bender·Luis M. A. Bettencourt
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Abstract

Conventional weak-coupling perturbation theory suffers from problems that arise from 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.

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Carl M. Bender, Luis M. A. Bettencourt. 1996-05-24. Multiple-Scale Analysis of the Quantum Anharmonic Oscillator. https://doi.org/10.1103/physrevlett.77.4114

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