Quantum Phase Operator and Phase States

TL;DR

This paper introduces a Hermitian quantum phase operator that aligns with classical phase behavior, providing explicit eigenstates expressed through Gegenbauer polynomials, advancing the understanding of quantum phase properties.

Contribution

It formulates a Hermitian quantum phase operator with proper classical correspondence and derives its eigenstates using Gegenbauer polynomials, filling a gap in quantum phase theory.

Findings

Hermitian quantum phase operator formulated with classical-like properties

Eigenstates expressed in Gegenbauer ultraspherical polynomials

Operator satisfies key trigonometric identities

Abstract

A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer ultraspherical polynomials in the number state representation.