Weyl quantization of anharmonic oscillators
- 1 May 1975
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 16 (5) , 1034-1043
- https://doi.org/10.1063/1.522656
Abstract
It is shown that polynomial self-interactions appearing repeatedly in the mathematical physics and chemical physics literature for the case of one degree of freedom can be treated in the formalism suggested by Weyl long ago, as was the case for the harmonic oscillator. New properties of the Schrödinger wavefunctions are derived, and appropriate schemes of approximation for the eigenvalue problem arise naturally in a nonperturbative way.Keywords
This publication has 14 references indexed in Scilit:
- New integral equation for the quartic anharmonic oscillatorLettere al Nuovo Cimento (1971-1985), 1974
- Phase transitions for one and zero dimensional systems with short-range forcesAnnals of Physics, 1974
- Anharmonic Oscillator. II. A Study of Perturbation Theory in Large OrderPhysical Review D, 1973
- Functional-Equation Approach to Canonical TheoriesPhysical Review D, 1971
- Coupling constant analyticity for the anharmonic oscillatorAnnals of Physics, 1970
- Generalized Anharmonic OscillatorJournal of Mathematical Physics, 1970
- Anharmonic OscillatorPhysical Review B, 1969
- Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field TheoryJournal of Mathematical Physics, 1960
- The exact transition probabilities of quantum-mechanical oscillators calculated by the phase-space methodMathematical Proceedings of the Cambridge Philosophical Society, 1949
- Quantum mechanics as a statistical theoryMathematical Proceedings of the Cambridge Philosophical Society, 1949