Abstract:
Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral
involving the associated Laguerre function. The method of brackets is used to evaluate the integral in
closed-form and to produce an expression for this average value as a finite sum.
The work of I.K. was supported in part by Fondecyt (Chile) Grants Nos. 1040368, 1050512 and 1121030, by DIUBB (Chile) Grant Nos. 102609, GI 153209/C and GI 152606/VC. V.H.M. acknowledges the partial support of NSF-DMS 1112656.
Received:November 23, 2016; in final form December 30, 2016; Published online January 5, 2017
Citation:
Ivan Gonzalez, Karen T. Kohl, Igor Kondrashuk, Victor H. Moll, Daniel Salinas, “The Moments of the Hydrogen Atom by the Method of Brackets”, SIGMA, 13 (2017), 001, 13 pp.
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\paper The Moments of the Hydrogen Atom by the Method of Brackets
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https://www.mathnet.ru/eng/sigma1201
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This publication is cited in the following 3 articles:
Gonzalez I., Kondrashuk I., Moll V.H., Recabarren L.M., “Mellin-Barnes Integrals and the Method of Brackets”, Eur. Phys. J. C, 82:1 (2022), 28
J.-Ch. Pain, F. Gilleron, “New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions”, J. Phys. B-At. Mol. Opt. Phys., 54:6 (2021), 065002
G. S. Adkins, M. F. Alam, C. Larison, R. Sun, “Coulomb expectation values in D=3 and D=3-2 epsilon dimensions”, Phys. Rev. A, 101:4 (2020), 042511
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