On the theory of the Schrödinger equation with the full set of relativistic corrections
A.A. Eremko1, L.S. Brizhik1, and V.M. Loktev1,2
1Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine 14-b Metrolohichna Str., Kyiv 03143, Ukraine
2National Technical University of Ukraine “KPI”, 37 Peremohy Ave., Kyiv 03056, Ukraine
Received December 12, 2017
All relativistic corrections to the Scrödinger equation which determine the interlink between spin and orbit of moving particles, are directly calculated from the Dirac equation using the spin invariant operators. It is shown that among the second order corrections there are not only the well-known Darwin and Thomas terms, but also the new ones. Only with the account of the latter corrections the energies found with the obtained spin-orbit interaction operator, coincide with the energies of the Dirac equation exact solution. The problem of electron spectrum in the quantum well type structures is studied in details and the physical reasons for the appearance of spin-orbit interaction operators in the Dresselhaus or Rashba form, are analyzed.
PACS: 03.65.Pm Relativistic wave equations;
Key words: Dirac equation, Schrödinger equation, spin-orbit interaction, spin splitting, two-dimensional electrons.
Published online: April 25, 2018