Perceptions of the Schrodinger Equation

TL;DR

This paper challenges the traditional view of the Schrödinger equation as a postulate, proposing a new interpretation based on virtual particle motions and wave superpositions, leading to a clearer mathematical foundation for quantum mechanics.

Contribution

It introduces a novel interpretation of quantum mechanics where the wavefunction is a superposition of virtual waves, clarifies the derivation of fundamental equations, and emphasizes the local and global nature of the theory.

Findings

Corrects the heuristic derivation of the Schrödinger equation

Defines the wavefunction as a superposition of virtual particle waves

Provides a clear mathematical foundation for quantum equations

Abstract

The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation cannot be a physical postulate, and we show that the heuristic derivations wrongly consider that the particle kinetic energy is proportional to the square of the momentum operator acting on the wavefunction. The correct term is proportional to the square of the momentum. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. As a result, quantum mechanics becomes a local and global theory, while in the traditional formulation it is a local theory. In several interaction settings we can tell what particle motions arise and explain the outcomes in simple and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.