Published August 21, 1984
| Version v1
Journal article
Higher-order JWKB approximations for radial problems
Description
The modified effective potential method for treating radial problems in the JWKB approximation is applied to the quartic oscillator defined by the potential V(r)=r4. The JWKB quantisation condition for the energy W is shown to be expressible as (2n, +1)π = AWsup(3/4)+B+CWsup(-3/4)+DWsup(-9/4)+O(Wsup(-15/4)). The l-dependent coefficients A, B, C and D are determined exactly by taking into account contributions from all orders. On inversion, the above series yields an explicit analytic formula for the energy levels. The formula is easily generalised to d dimensions, and found to reproduce known numerical eigenvalues extremely well. (author)
Additional details
Additional titles
- Subtitle (English)
- 2. The quartic oscillator
Publishing Information
- Journal Title
- J. Phys., A (London). Math. Gen.
- Journal Volume
- 17
- Journal Issue
- 12
- Series
- J. Phys., A (London). Math. Gen.
- Journal Page Range
- 2493-2503
- ISSN
- 0305-4470
INIS
- Country of Publication
- United Kingdom
- Country of Input or Organization
- United Kingdom
- INIS RN
- 16007448
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- ANALYTICAL SOLUTION; ANHARMONIC OSCILLATORS; EIGENVALUES; ENERGY; ENERGY LEVELS; OSCILLATION MODES; POTENTIALS; QUANTIZATION; SCHROEDINGER EQUATION; SPHERICAL CONFIGURATION; WAVE FUNCTIONS
- Descriptors DEC
- CONFIGURATION; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS