Abstract
We show how comparison equation technique can be used to overcome a difficulty that arises in the neighborhood of the origin in the numerical integration of a Schrödinger-like differential equation by means of the phase-amplitude method, when the effective potential behaves as 1/(4z 2) close to the origin. These results are applied to the calculation of the energy eigenvalues of a two-dimensional anharmonic oscillator.
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References
Milne, W.E., Phys. Rev. 35 (1930), 863–867.
Wilson, H.A., Phys. Rev. 35 (1930), 948–956.
Young, L.A., Phys. Rev. 38 (1931), 1612–1614.
Young, L.A., Phys. Rev. 39 (1932), 455–457.
Wheeler, J.A., Phys. Rev. 52 (1937), 1123–1127.
Fröman, N., Fröman, P.O., and Linnaeus, S., Phase-integral formulas for the regular wave function when there are turning points close to a pole of the potential. This is Chapter 6 in the present monograph.
Fröman, N. and Fröman, P.O., Phase-integral approximation of arbitrary order generated from an unspecified base function. This is Chapter 1 in the present monograph.
Bell, S., Davidson, R., and Warsop, P.A., J. Phys. B3 (1970), 113–122.
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Fröman, P.O., Hökback, A., Fröman, N. (1996). Phase-Amplitude Method Combined with Comparison Equation Technique Applied to an Important Special Problem. In: Phase-Integral Method. Springer Tracts in Natural Philosophy, vol 40. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2342-9_8
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DOI: https://doi.org/10.1007/978-1-4612-2342-9_8
Publisher Name: Springer, New York, NY
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