NUMERICAL ANALYSIS OF ENERGY LEVELS OF QUANTUM PARTICLE IN FIELD OF TWO-DIMENSIONAL DIPOLE

Abstract

Aim of the paper is a numerical investigation of energy levels of a quantum particle in a field of a two-dimensional dipole, based on the numerical algorithm proposed for solving the full two-dimensional Schrцdinger equation. Methodology. With the help of special expansion of a wave function the two-dimensional Schrцdinger equation was transformed to the Sturm-Liouville boundary problem for the system of differential equations. The method of inverted iterations with a shift was applied to the matrix eigenvalues search problem, that was obtained after a finite-difference approximation of the derivatives. Results. The low-lying energy levels and the corresponding wave functions of a quantum particle in a field of a two-dimensional dipole were determined. Research implications. The energy levels of bound states of a quantum particle in a field of a two-dimensional dipole were obtained using the proposed numerical algorithm. The agreement was obtained with the work of other author, where the variational approach was used, for which there is no error estimates of the calculated values relative to the exact solution. The calculations that were carried out by us with known convergence and error estimates fill this gap.

Keywords

• two-dimensional Schrödinger equation
• anisotropic interactions
• numerical algorithm