Schrdinger equations on R-3 x M with non-separable potential

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    J. Math. Chem.

    Keywords

    Hydrogen atom; Schrodinger equation; Eigen value problem; Non-separable; potential; Compact extra dimensions; D-DIMENSIONAL ATOM; KAHLER-MANIFOLDS; HYDROGEN-ATOM; WAVE-FUNCTIONS; STATES; OSCILLATOR; ORBITALS; Chemistry, Multidisciplinary; Mathematics, Interdisciplinary; Applications

    Abstract

    We consider the problem of defining the Schrodinger equation for a hydrogen atom on R-3 x M where M denotes an m dimensional compact manifold. In the present study, we discuss a method of taking non- separable potentials into account, so that both the non- compact standard dimensions and the compact extra dimensions contribute to the potential energy analogously to the radial dependence in the case of only non- compact standard dimensions. While the hydrogen atom in a space of the form R-3 x M, where M may be a generalized manifold obeying certain properties, was studied by Van Gorder (J Math Phys 51:122104, 2010), that study was restricted to cases in which the potential taken permitted a clean separation between the variables over R-3 x M. Furthermore, though there have been studies on the Coulomb problems over various manifolds, such studies do not consider the case where some of the dimensions are non- compact and others are compact. In the presence of nonseparable potential energy, and unlike the case of completely separable potential, a complete knowledge of the former case does not imply a knowledge of the latter.

    Journal Title

    Journal of Mathematical Chemistry

    Volume

    50

    Issue/Number

    6

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1420

    Last Page

    1436

    WOS Identifier

    WOS:000303892200007

    ISSN

    0259-9791

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