Application of Schrödinger Wave Equation to Predict Wave Function on the Influence of Displacement

Abstract

This research work contains a review of the Finite-Difference Time-Domain method as applied to the time-dependent Schrödinger wave equation, and the basic update equations are derived in their standard form. A simple absorbing boundary condition was formulated and shown to be effective with narrowband wave functions. The stability criterion was derived from a simple, self explaining perspective and found to give better efficiency than earlier attempts. Conclusively, the idea of simulation using MATLAB gives room for application of computer program that simplified the one-dimensional time dependent Schrödinger wave equation using FDTD method, also classical laws of physics to predict time evolution of expectation values were applied in this study.

Key words: Application, Schrödinger, wave equation, predict, wave function, influence, displacement