THE COMPUTER – ASSISTED SOLUTION OF THE ONE – DIMENSIONAL SCHRÖDINGER EQUATION TAKING INTO ACCOUNT TUNNELING EFFECTS

Abstract

The general scheme of the method of integration of the second order ordinary differential equations with regular singular points is outlined. The algorithm of finding a general solution of the second order differential equation with regular singular points is given. The Schr dinger equation for anharmonic oscillator with the potential of the fourth, sixth and eighth degrees of non-linearity is considered, the values of its energy spectrum are found.

Keywords

• ordinary differential equation
• anharmonic oscillator
• wave function
• generalized power series