A Causal Interpretation Of A Quantum Harmonic Oscillator

Abstract

Some of the mathematical theories underlying the causality of a two level quantum system, are shown with respect to the Schrodinger Time Dependent Equation. To this equation, complex number theory is applied, leading to a formulation of the classical Hamilton-Jacobi equation which includes a new quantum potential term, which justifies the introduction of hidden variables. From this theory, it is then possible to develop a computer software model of the evolution of the system co-ordinates of particles, or the particles in a quantum system.

The Causal Interpretation is illustrated by means of a common example, in this case, a two level quantum harmonic oscillator, to which time dependent perturbation theory is applied. In this example, the particle trajectories are demonstrated firstly by analytical methods and then by graphical display; both by means of a computer software model.