Higher-Order Corrections of the Modified WKB Approximation to the Solution of the Repulsive Singular Potential

P. Lu; S. S. Wald

doi:10.1103/PhysRevD.8.4371

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Higher-Order Corrections of the Modified WKB Approximation to the Solution of the Repulsive Singular Potential

P. Lu and S. S. Wald

Department of Physics, Arizona State University, Tempe, Arizona 85281

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Phys. Rev. D 8, 4371 – Published 15 December, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.4371

Abstract

We extend the modified WKB approximation due to Miller and Good to the $ℏ^{4}$ order for the scattering case by the repulsive inverse-fourth-power potential. Instead of describing the higher-order terms by the phase-integral formula in terms of line integrals with a specific contour in a complex plane, we present the formula here in terms of definite integrals.

References (6)

P. Lu and S. S. Wald, J. Math. Phys. 13, 646 (1972)
S. C. Miller, Jr. and R. H. Good, Jr., Phys. Rev. 91, 174 (1953)
W. M. Frank, A. J. Land, and R. M. Spector, Rev. Mod. Phys. 43, 36 (1971)
J. A. Coombs and S. H. Lin, J. Chem. Phys. 54, 2285 (1971)
E. Del Giudice and E. Galzenati, Nuovo Cimento 40, 739 (1965)
P. Lu and E. M. Measure, Phys. Rev. D 5, 2514 (1972)

[c1] P. Lu and S. S. Wald, J. Math. Phys. 13, 646 (1972)

[c2] S. C. Miller, Jr. and R. H. Good, Jr., Phys. Rev. 91, 174 (1953)

[c3] W. M. Frank, A. J. Land, and R. M. Spector, Rev. Mod. Phys. 43, 36 (1971)

[c4] J. A. Coombs and S. H. Lin, J. Chem. Phys. 54, 2285 (1971)

[c5] E. Del Giudice and E. Galzenati, Nuovo Cimento 40, 739 (1965)

[c6] P. Lu and E. M. Measure, Phys. Rev. D 5, 2514 (1972)

Physical Review D

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Higher-Order Corrections of the Modified WKB Approximation to the Solution of the Repulsive Singular Potential

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