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.
Journal Title
Journal of Mathematical Physics
Volume
51
Issue/Number
12
Publication Date
1-1-2010
Document Type
Article
DOI Link
Language
English
First Page
12
WOS Identifier
ISSN
0022-2488
Recommended Citation
Van Gorder, Robert A., "Wave functions and energy spectra for the hydrogenic atom in R-3 x M" (2010). Faculty Bibliography 2010s. 884.
https://stars.library.ucf.edu/facultybib2010/884
Accessibility Statement
This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.
Comments
Authors: contact us about adding a copy of your work at [email protected]