Abstract
The radial generalization of Dunham's one-dimensional WKB quantization condition, including second- and third-order corrections is derived using the Langer transformation. It is found that, although the first-order integral can be obtained from Dunham's results by substituting (l=12)2 for l(l+1) in the effective potential, there is no choice of effective potential that leads to the correct second- and third-order integrals. It is suggested that all previous eigenvalue calculations using higher-order WKB approximations for the radial case should be reinvestigated. It is shown that the second- and third-order integrals identically vanish for the hydrogen atom and the three-dimensional harmonic oscillator, as expected.
Original language | English (US) |
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Pages (from-to) | 171-173 |
Number of pages | 3 |
Journal | Physical Review |
Volume | 164 |
Issue number | 1 |
DOIs | |
State | Published - 1967 |
Externally published | Yes |
ASJC Scopus subject areas
- General Physics and Astronomy