On the existence of a non-relativistic hermitian time operator

TL;DR

This paper proposes a hermitian time operator within non-relativistic quantum mechanics, exploring its implications for the flow of time, classical correspondence, and quantum state transitions, revealing novel insights into the nature of time and particle behavior.

Contribution

It introduces a non-relativistic hermitian time operator and analyzes its implications for quantum dynamics and particle perception of time, aligning with classical physics and revealing new phenomena.

Findings

Time flows at a constant rate according to the Heisenberg equation

Massless particles with momentum experience timelessness in their frame

Electrons can instantaneously transition between eigenstates

Abstract

The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with classical expectations,when Bohr's correspondence principle is invoked.Further,it is shown that a massless free particle with non-zero momentum experiences timelessness in its own frame of reference whereas a negatively massive particle perceives forwardness of time.Moreover,application to quantum harmonic oscillators shows instantaneous transition of electrons from one eigenstate to another.