WKB approximation for bound states by Heisenberg matrix mechanics
- 1 January 1978
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 19 (1) , 292-297
- https://doi.org/10.1063/1.523503
Abstract
The WKB approximation for bound states is derived from Heisenberg matrix mechanics. It is shown that the result can be obtained from the Bohr–Sommerfeld quantization of a suitably chosen solution of the classical equations of motion. It is also derived from the commutation relation and from a quantum form of Hamilton’s variational principle.Keywords
This publication has 18 references indexed in Scilit:
- Anharmonic-oscillator energies with operator recursion mechanicsPhysical Review D, 1976
- Nonlinear Schrödinger equation: A testing ground for the quantization of nonlinear wavesPhysical Review D, 1976
- General techniques for single and coupled quantum anharmonic oscillatorsJournal of Mathematical Physics, 1975
- Matrix mechanics as a practical tool in quantum theory: The anharmonic oscillatorPhysical Review D, 1975
- Quantum expansion of soliton solutionsPhysical Review D, 1975
- Accurate-Order Iterative Method for Nonlinear OscillatorsPhysical Review D, 1973
- Quantum mechanics of the anharmonic oscillatorJournal of Mathematical Physics, 1973
- Phase-Integral Approximation in Momentum Space and the Bound States of an Atom. IIJournal of Mathematical Physics, 1969
- Exact Quantization ConditionsJournal of Mathematical Physics, 1968
- Phase-Integral Approximation in Momentum Space and the Bound States of an AtomJournal of Mathematical Physics, 1967