Quantal two-center Coulomb problem treated by means of the phase-integral method. II. Quantization conditions in the symmetric case expressed in terms of complete elliptic integrals. Numerical illustration

Athavan, N. ; Lakshmanan, M. ; Froman, N. (2001) Quantal two-center Coulomb problem treated by means of the phase-integral method. II. Quantization conditions in the symmetric case expressed in terms of complete elliptic integrals. Numerical illustration Journal of Mathematical Physics, 42 (11). pp. 5077-5095. ISSN 0022-2488

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Official URL: http://link.aip.org/link/?JMAPAQ/42/5077/1

Related URL: http://dx.doi.org/10.1063/1.1399295

Abstract

The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that the charges of the Coulomb centers are equal. The evaluation of the integrals is facilitated by the knowledge of quasiclassical dynamics. The resulting quantization conditions involving complete elliptic integrals are solved numerically to obtain the energy eigenvalues and the separation constants of the 1sσ and 2pσ states of the hydrogen molecule ion for various values of the internuclear distance. The accuracy of the formulas obtained is illustrated by comparison with available numerically exact results.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:19569
Deposited On:22 Nov 2010 12:23
Last Modified:17 May 2016 04:05

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