Multiple-Scale Analysis of the Quantum Anharmonic Oscillator
Abstract
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.
- Publication:
-
Physical Review Letters
- Pub Date:
- November 1996
- DOI:
- 10.1103/PhysRevLett.77.4114
- arXiv:
- arXiv:hep-th/9605181
- Bibcode:
- 1996PhRvL..77.4114B
- Keywords:
-
- High Energy Physics - Theory;
- High Energy Physics - Phenomenology;
- Quantum Physics
- E-Print:
- 12 pages, Revtex, no figures, available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers/papers_95-6_.html