The Ordering Ambiguity

TL;DR

This paper revisits the ordering ambiguity in the kinetic energy operator for quantum particles with position-dependent mass, proposing a new form as a superposition of acceptable ordering parameters.

Contribution

It introduces a novel form of the kinetic energy operator as a superposition of different ordering parameter values, addressing the ambiguity.

Findings

Proposes a continuous or discrete superposition of ordering parameters.

Provides a new formulation for the kinetic energy operator.

Addresses the longstanding ordering ambiguity in quantum mechanics.

Abstract

The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable values for the ordering parameters.