Title

Police Use Of Force And Officer Injuries: Comparing Conducted Energy Devices (Ceds) To Hands- And Weapon-Based Tactics

Keywords

Compact extra dimensions; Eigen value problem; Hydrogen atom; Non-separable potential; Schrödinger equation

Abstract

We consider the problem of defining the Schrödinger equation for a hydrogen atom on ℝ 3 × 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 × 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 and 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 non-separable 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. © 2012 Springer Science+Business Media, LLC.

Publication Date

6-1-2012

Publication Title

Police Quarterly

Volume

15

Issue

6

Number of Pages

115-136

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1177/1098611112442807

Socpus ID

84860723391 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84860723391

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