Modified Born-Jordan Method For Constructing The Commutation Relation Of Coordinate and Momentum

TL;DR

This paper proposes a modified Born-Jordan method to construct the quantum commutation relation between coordinate and momentum, addressing limitations of the original approach and introducing a new expression for the Bohr quantum condition.

Contribution

The work introduces a novel modification to the Born-Jordan method, providing a new way to derive the quantum condition using matrix elements of the integral of momentum and position.

Findings

Reveals limitations of the original Born-Jordan method

Develops a modified approach for quantum condition construction

Proposes a new expression for the Bohr quantum condition

Abstract

The Born-Jordan method for constructing the quantum condition of the Matrix Mechanics is pointed out to be inappropriate in the present work. We modify this method and reconstruct the quantum condition by setting up a new expression for the Bohr quantum condition with the help of the (n,n) elements of the matrix $\oint\hat{p}(t){\rm d}\hat{x}(t)$.