The Phase Method: for Numerical Solution of the Schrödinger Equation

This book introduces a simple and robust new computational method, the Phase Method (PM), for numerical solving the time independent Schrödinger Equation for the energy levels and wave functions in 1D, 2D/3D-central, and higher dimensional separable potentials. Detailed explanations are presented of why the PM works, how to use it effectively, and how it relates to conventional methods. Various examples are given, and the PM is used to verify new and useful approximate semiclassical formulae that are first given here. The book is expected to be useful to students exploring quantum mechanics, and also to high school teachers, college professors, working scientists, engineers, and nanotechnologists, with applications to quantum physics and chemistry, materials science, nanotechnology and nanophotonics, and related fields. Working example code in Python and Mathematica is given in appendices. Read more