Basic quantum Hamiltonian's relativistic 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.