Revisiting quantum relativistic effects from phase transition by the catastrophe theory

Abstract

In this paper we start from the Schrödinger equation to revisit some classical quantum mechanics from the perspective of phase transition process. Here the relativistic effect of particles moving at high speed can be regarded as the phase transition process when the velocity variable increases. Considering that the catastrophe theory could describe qualitatively any phase transition process, we adopt the simplest folding catastrophe type as the potential function in the Schrödinger equation to obtain a revised Schrödinger relativistic equation through the dimensionless analysis first, and then further to derive out the steady-state Klein-Gordon equation and Dirac relativistic equation gradually. These results reveal that the quantum relativistic effect could be considered as the phase transition process, which could be described by adopting the catastrophe models as the potential function in the classical Schrödinger equation.