#### 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

## Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu