Time Dependent Dirac Equation FEM Solutions for Relativistic Quantum Mechanics

A. J. Kalinowski [1],
[1] Consultant, East Lyme, CT, USA
Published in 2017

The paper illustrates the use of COMSOL (via the “Coefficient-Form PDE” option) for obtaining the relativistic quantum mechanics wave function Ψm(x,y,z,t), m=1,4 as a solution to the time dependent Dirac equations. Once having Ψm(x,y,z,t), it can be used to compute the probability density ρd=Σ|Ψm|2of a particle being at a specific point within the spatial field under consideration. Six problems are solved to illustrate solving Dirac equations; the first three are validation FEM - exact solution comparisons and the last three are more complex ones where no comparison closed form solution is available.