Kinematic relativity of quantum Hamiltonian

TL;DR

This paper revises the relativistic quantum Hamiltonian by using a proper kinetic energy expression, leading to a more consistent operator and new potential insights into quantum phenomena.

Contribution

It introduces a corrected relativistic kinetic energy operator that aligns with special relativity, improving the quantum Hamiltonian framework.

Findings

New form of relativistic kinetic energy operator

Consistent relation with special relativity

Potential for novel quantum phenomena descriptions

Abstract

It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the kinetic energy operator which relation with the ususal one is consistent with corresponding relation of kinetic energies in special relativity theory. The Schr\"odinger equation with this operator gives new interesting possibilities for quantum phenomena description.