Solutions of the three-dimensional time-independent Schrödinger equation

Fakir Chand, Shubham Mishra

H. T. Williams

I present a method in the spirit of Green’s functions for generating bound state solutions to the Schrödinger equation. The method is demonstrated by generating ground state and excited state solutions to the one-dimensional, time-independent Schrödinger equation. Its applicability to the radial equation for two and three dimensions is also discussed.

Ismail Abbas

We have shown in previous papers that B- matrix string mechanics, which is the product of a numerical statistical method called the Cairo technique, can be successfully applied to solve the most general form of the diffusion equation of heat as well as the time- independent equation. Schrödinger equation. In this paper we examine the extension of matrix chains from the Cairo technique to the solution of the time-dependent Schrödinger equation. Numerical results for a quantum particle in a three- dimensional box are presented and are intended to be strikingly precise.

S. Brandt, Hans Dieter Dahmen

Emanullah Hızel, Nurettin Cenk Turgay, Bahri Guldoùgan

Schrödinger-Newton (SN) equations are modifications of the Schrödinger equation proposed by Roger Penrose involved in a gravitationally-induced wave function collapse scheme. In this paper, the three dimensional time independent Schrödinger-Newton (SN) equation is analyzed. The Lie group formalism is applied to deduce symmetries of the time indepen-dent SN equation for three dimensional case. One and two dimensional optimal systems and reduced equations are obtained.