Expectation value dynamics within real Hilbert space quantum mechanics

TL;DR

This paper explores the dynamics of expectation values in real Hilbert space quantum mechanics, extending the formalism to complex and quaternionic wave functions, and verifying its consistency through various physical principles.

Contribution

It introduces a real Hilbert space framework for quantum expectation value dynamics, including generalized operators and consistency checks, expanding the theoretical foundation of quantum mechanics.

Findings

Verified formalism consistency via continuity equation and classical limit

Extended quantum Lorentz force and Virial theorem to real Hilbert space

Introduced generalized position and angular momentum operators

Abstract

Dynamic equations concerning physical expectation values have been examined in terms of the real Hilbert space approach to quantum mechanics. The considered cases involve complex wave functions, as well as quaternionic wave functions. The consistency of the formalism has been verified in terms of the continuity equation, the classical limit, and generalizations of the quantum Lorentz force, and the Virial theorem. Besides testing the consistency of the real Hilbert space approach, generalized position and angular momentum operators have been introduced, and inspire exciting directions for further research.