Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

Details Multiple-Scale Analysis of the Quantum Anharmonic Oscillator Multiple-Scale Analysis of the Quantum Anharmonic Oscillator

1996-05-24

arxiv.org/abs/hep-th/9605181v1

Phys.Rev.Lett. 77 (1996) 4114-4117

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Revtex, no figures, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://e

Scientific paper

10.1103/PhysRevLett.77.4114

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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