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Completeness of the Coulomb wave functions in quantum mechanics

Mukunda, N (1978) Completeness of the Coulomb wave functions in quantum mechanics. In: American Journal of Physics, 49 (6). pp. 910-913.

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We give an explicit, direct, and fairly elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses only some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory; therefore it would form useful supplementary reading for a graduate course on quantum mechanics.

Item Type: Journal Article
Publication: American Journal of Physics
Publisher: American Institute of Physics
Additional Information: Copyright of this article belongs to American Institute of Physics.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited: 21 Sep 2010 06:57
Last Modified: 21 Sep 2010 06:57
URI: http://eprints.iisc.ac.in/id/eprint/32281

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