Schrdinger equations on R-3 x M with non-separable potential
Abbreviated Journal Title
J. Math. Chem.
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
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 of Mathematical Chemistry
"Schrdinger equations on R-3 x M with non-separable potential" (2012). Faculty Bibliography 2010s. 3421.