Analytical Solution of the Position Dependent Mass Schr\"{o}dinger Equation With a Hyperbolic Tangent Potential

Abstract

An analytical solution of the position dependent mass Schrödinger equation with a hyperbolic tangent potential is presented. The state energy and the corresponding wave function are obtained using the Nikiforov-Uvarov method. The energy eigenvalues and eigenfunctions are discussed and results are presented for some values of potential parameters.

Rothe-Maruyama Difference Scheme for the Stochastic Schr\"{o}dinger Equation

“…In the literature, stochastic and deterministic type Schrödinger equations have been extensively studied by many researchers (see [2], [3], [6], [11] and the references given therein). Although, in any Hilbert space, numerical approximation of abstract stochastic Schrödinger equation, using Rothe-Maruyama difference scheme has not been studied yet.…”