Basic quantum Hamiltonian's relativistic corrections

TL;DR

This paper explores how relativistic corrections to the kinetic energy operator affect the spectra of fundamental quantum Hamiltonians, revealing significant modifications in some cases.

Contribution

It introduces relativistic and pseudo-relativistic kinetic energy operators derived from Dirac's equation and analyzes their impact on quantum spectra.

Findings

Relativistic corrections can significantly alter quantum spectra.

The pseudo-relativistic operator in Schrödinger equation shows notable effects.

Some spectra experience remarkable modifications due to these corrections.

Abstract

After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum expressions allows us to define the non-relativistic, relativistic and pseudo-relativistic (present in Schr\"odinger equation) kinetic energy operators. Consequences of kinetic energy operator's correction for spectra of basic quantum Hamiltonians are investigated. In some cases this correction can produce remarkable spectra modifications.