Waves, analytical signals, and some postulates of quantum theory

TL;DR

This paper applies analytical signal theory to the Schrödinger wavefunction, deriving quantum operators and measurement probabilities solely from wave-particle duality and relativistic covariance, without additional quantum postulates.

Contribution

It introduces a novel approach using analytical signals to derive quantum operators and measurement rules from fundamental principles.

Findings

Derivation of quantum energy and momentum operators from wave-particle duality and covariance.

Quantum measurement probabilities obtained without traditional postulates.

Application of characteristic function formalism to quantum measurement theory.

Abstract

In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the quantum energy and momentum operators for a single nonrelativistic particle. Without using any more quantum postulates, and employing the formalism of the characteristic function, we also derive the quantum-mechanical prescription for the measurement probability in such cases.