Solution of the 1D Schrödinger equation in semiconductor heterostructures using the immersed interface method

Due to the enormous progress in computer technology and numerical methods that has been achieved over the past several decades, the use of numerical simulation methods in all scientific disciplines gain more and more importance. In the physics field, these methods have provided remarkable numerical solutions to problems considered analytically intractable. The solution of the Schrödinger equation in semiconductor heterostructures is a good example. However, many of these numerical schemes are cumbersome to implement for nonexperts in numerical computing. With this reason as motivation, a novel method simple enough to implement yet powerful enough to solve Schrödinger equation in semiconductor devices with high accuracy is presented herein.