## Basic quantum Hamiltonian's relativistic corrections    [PDF]

Gintautas P. Kamuntavičius
By analysing Dirac's equation it follows that well-known quantum-mechanical momentum operator is associated with relativistic momentum rather than non-relativistic one. Consideration of relativistic energy and momentum expressions provides the possibility to define the non-relativistic, relativistic and pseudo-relativistic (present in Schr\"odinger equation) kinetic energy operators. Consequences of kinetic energy operator's correction investigated are for spectra of basic quantum Hamiltonians describing particle, moving in external field, defined by spherical well, harmonic oscillator and Coulomb potentials. It is shown that in some cases relativistic kinetic energy correction can produce remarkable Schr\"odinger equation spectrum changes.
View original: http://arxiv.org/abs/1302.0491