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Generalized Levinson theorem for singular potentials in two dimensions

“…Levinson theorem was validated for the Schrödinger equation [17], the Schrödinger equation with a nonlocal interaction [18], the Klein-Gordon equation [19], and the Dirac equation [20], even in the presence of solitons [21]. The Levinson theorem was implemented in the (1+1) gauge theory to calculate the fractional and integer fermion numbers [22].…”

“…Moreover there exists an extension of the Levinson theorem for the Schrödinger equation in D dimensions. There are several methods for studying the lower-dimensional Levinson theorem: the Jost function method [27], the Green function method [20,23,26,28], and the Sturm-Liouville theorem [17,18,19,24,25,29]. Levinson's relation for the partial wave phase has the usual form, as for the 3D case; but the halfbound state for the p-wave (l = 1) contributes exactly like the bound state and gives an additional π to Levinson's relation [28].…”

Solutions of Schrodinger equation for the modified Mobius square plus Kratzer potential

“…In theoretical physics and other physics-related fields, much research interest has been directed toward obtaining and discussing the exact solutions of Schrodinger wave equation for different potentials, during the past years [1][2][3][4][5]. The reason is because the solutions contain sufficient information to explain the quantum system under probe.…”

Electron Escaping in the Magnetically Confined Electron Cloud

“…Artsimovich from the former Soviet Union Scientific Centre "Kurchatov Institute" completed the first magnetic confinement device named Tokamak in 1954 according to this idea. Tokamak is a typical representative of magnetic confinement device [3][4][5][6]. The ultimate goal of the magnetic confinement is to realize nuclear fusion.…”