Title

Wave functions and energy spectra for the hydrogenic atom in R-3 x M

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

J. Math. Phys.

Keywords

QUANTUM-FIELD THEORY; SPACE DISTRIBUTION FUNCTION; D-DIMENSIONAL ATOM; KAHLER-MANIFOLDS; PHASE-SPACE; RICCI CURVATURE; WIGNER-FUNCTION; MOMENTUM-SPACE; PERIODIC-TABLE; COMPACT; Physics, Mathematical

Abstract

We consider the hydrogenic atom in a space of the form R-3 x M, where M may be a generalized manifold obeying certain properties. We separate the solution to the governing time-independent Schrodinger equation into a component over R-3 and a component over M. Upon obtaining a solution to the relevant eigenvalue problems, we recover both the wave functions and energy spectrum for the hydrogenic atom over R-3 x M. We consider some specific examples of M, including the fairly simple D-dimensional torus T D and the more complicated Kahler conifold K in order to illustrate the method. In the examples considered, we see that the corrections to the standard energy spectrum for the hydrogen atom due to the addition of higher dimensions scale as a constant times 1/L-2, where L denotes the size of the additional dimensions. Thus, under the assumption of small compact extra dimensions, even the first energy corrections to the standard spectrum will be quite large. (C) 2010 American Institute of Physics. [doi:10.1063/1.3520507]

Journal Title

Journal of Mathematical Physics

Volume

51

Issue/Number

12

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

12

WOS Identifier

WOS:000285768900004

ISSN

0022-2488

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