A discussion on a dynamic vacuum model: Derivation of Helmholtz equation from Schrodinger equation

In this paper, Madelung's quantum Euler equations will be re-derived, which will be shown to lead to the familiar form of the acoustic wave equation for a medium. A model of the density variation in the vacuum field around the nucleus of the hydrogen atom is then introduced and used to create a simplified representation of the atom in COMSOL. The time-independent form of the acoustic wave equation (Helmholtz equation) is used to find the eigenfrequency acoustic modes of the simulated atom. The analysis technique for the single atom case is extended to build a model of molecular hydrogen, and the numerical analysis results are presented and discussed. The paper concludes with some speculative discussion on the nature and make up of the dynamic vacuum medium being modeled around the hydrogen nucleus. This polar form of the Schrodinger equation can be separated into its real and imaginary parts respectively: