Abstract
The exact solution of the Schrödinger equation is derived for the case of a central potential under rather weak restriction on it. The solution is given in a form of a simple series which converges strongly and it is suitable for calculation of phase shifts and eigenvalues. Also, as the derivation of the solution is purely algebraic its analytical continuation in the energy or angular momentum complex plane is straightforward.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kanellopoulos, E. J., Kanellopoulos, Th. V., Wildermuth, K.: Commun. math. Phys.24, 225 (1972).
Newton, R. G.: J. Math. Phys. Vol.1, 319 (1960).
See for example Squires, E.: Complex angular momenta and particle physics. Frontiers in Physics. New York-Amsterdam: W. A. Benjamin Inc. 1963.
Bateman Project Higher transcendental functions, Vol. II. New York: McGraw Hill Book Co. Inc. 1958.
Bateman Project Tables of integral transforms, Vol. I. p. 333 (43). New York: McGraw Hill Book Co. Inc. 1953.
Watson, G. N.: Theory of Bessel functions, Second Ed., p. 446. Cambridge: University Press 1958.
Ta-You-Wu, Ohmura, T.: Quantum theory of scattering, p. 45. In this book further references are found. Englewood Cliffs, N.J.: Prentice Hall International 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kanellopoulos, E.J., Kanellopoulos, T.V. & Wildermuth, K. Exact solution of the Schrödinger equation with a central potential. Commun.Math. Phys. 24, 233–242 (1972). https://doi.org/10.1007/BF01877715
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01877715