On the interaction of the type λx2/(1+g x2)

Abstract

The ground state and the first two excited state energy levels for the interaction of the type λx2/(1+gx2) have been calculated nonperturbatively as the eigenvalues of the one-dimensional Schrödinger operator defined by Au=−u′′+x2u+λx2u/(1+gx2). The Ritz variational method in combination with the Givens–Householder algorithm has been used for numerical computations.

A non-linear oscillator with quasi-harmonic behaviour: two- andn-dimensional oscillators

“…We close this section by solving the two-dimensional free-particle motion determined by two-dimensional kinetic function (7).…”

Application of the Inner Product Technique to Some Nonpolynomial Potentials for Multidimensional Quantum Systems

“…(1), has recently been studied by many authors using different techniques. Mitra [1] cal-V Ϫ (x; g), g Ն 0, Ͱ Ͼ 2 (in order that V Ϫ (x, g) Ǟ ȍ as x 2 Ǟ ȍ). Auberson and Boissiere [15] calculated the ground culated the ground state and first two excited states using the Ritz variational method in combination with a Givens-state energy level for a large range of values of Ͱ and g, using several methods.…”

“…As summarized by Mitra [1], this type of interaction occurs in several areas of physics. In particular, this type There are a variety of techniques which have been emof potential occurs when considering models in laser theory ployed to calculate and to investigate the one-dimen- [12] and also to a zero-dimensional field theory with a sional potentials nonlinear Lagrangian [13].…”

A Numerical Approach for the Solution of Schrödinger Equation With Pseudo-Gaussian Potentials

“…The purpose of this presentation is to investigate the stability for the values of energy levels considering different numbers of terms in the analytical solution and comparing them with those obtained by computational technique. We have chosen the finite difference methods for computing approximate eigenvalues of equation (1). In this case of quasi-exactly solvable systems a numerical verification upon the convergence of the solution is required.…”

“…For most potential function the equation has to be solved by different suitable ways. Several lines of approach have been followed in the study of SE for different types of potentials such as: variational [1,2] and perturbational schemes [3], also combined with direct numerical methods [4] and series solutions [5] as well as the recently approach to solve SE into momentum representation [6]. Also there is a geometic approach to solve SE, known as geometric quantisation [7].…”