Higher-order JWKB approximations for radial problems. III. The r2moscillator
- 21 April 1985
- journal article
- addendum
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (6) , 1041-1045
- https://doi.org/10.1088/0305-4470/18/6/027
Abstract
For pt.II see ibid., vol.17, p.2493, 1984. Higher-order JWKB approximations are applied to the calculation of energy levels of an oscillator with the potential V(r)=r2m (m integer). The JWKB quantisation condition for the energy W is shown to be expressible as (n+3/2) pi =AX+BX-1+CX-3+. . . where X=W(m+1)2m/. The l-dependent coefficients A, B, C are determined exactly by taking into account contributions from all orders. On inversion the above series yields an explicit analytical formula for the energy levels. Extension of the result to d dimensions is immediate.Keywords
This publication has 3 references indexed in Scilit:
- Higher-order JWKB approximations for radial problems. I. Modification of the effective potentialJournal of Physics A: General Physics, 1984
- Higher-order JWKB approximations for radial problems. II. The quartic oscillatorJournal of Physics A: General Physics, 1984
- Numerological analysis of the WKB approximation in large orderPhysical Review D, 1977