Graphical Interpretation of the Schrödinger Equation

Haruo Hosoya, Mayumi Hirose

Subhagaurab Roy, Rupam Sen, Ashim Kalyan +2 more

Christian Bauckhage, Rafet Sifa

Abstract In this chapter, we familiarize ourselves with certain aspects of quantum weirdness, namely energy quantization, quantum tunneling, and quantum superposition. To this end, we consider three didactic examples of quantum systems, solve the respective scenario specific Schrödinger equations, and (mathematically and graphically) analyze and interpret the results we obtain therefrom. Despite of the utter simplicity of our scenarios, two of them already defy analytic solutions. Since this is not uncommon when trying to solve Schrödinger equations for specific settings, we also discuss simple numerical methods for Schrödinger equation solving and present code examples which implement those.

Wojciech Szczepankiewicz

A graphical interpretation of the time-independent Schroumldinger equation in the Cartesian coordinate system for the explicitly set wave function of the ground state and selected excited states of the hydrogen has been presented. It was shown that the equation left-sidedly multiplied by the function psi allows to find its didactic connection with the course of the beam of light emitted by the hydrogen atom in the measuring system of the spectroscope equipped with a prism.

Doug Jensen

John C. Morrison