On the position representation of mechanical power, force and torque operators

TL;DR

This paper develops a quantum operator framework for mechanical power, force, and torque in position space, introducing new relations and analogs to energy and momentum, grounded by a fundamental constant.

Contribution

It introduces a novel operator representation for power, force, and torque in quantum mechanics, extending the understanding of their position-space formulations.

Findings

Derived quantum impulse equation and related operator relations.

Introduced power-frequency and force-wavelength analogs.

Established correspondence between torque operator and orbital angular momentum.

Abstract

Quantizing the transfer of energy and momentum between interacting particles, we obtain a quantum impulse equation and relations that the corresponding mechanical power, force and torque satisfy. In addition to the energy-frequency and momentum-wavelength relations, we introduce the power-frequency and force-wavelength analogs, respectively. Further, we obtain an operator representation for the mechanical power and impact force in the position space and discuss their correspondence with the relevant momentum operator. The position representation of the torque operator and its relation to the orbital angular momentum operator is also considered. The results are grounded by the presence of a constant that appears as fundamental as the Planck's constant to all obtained relations.