On the theory of the Schroedinger equation with the full set of relativistic corrections

All relativistic corrections to the Scr{\"o}dinger 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 we...

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Bibliographic Details
Published inarXiv.org
Main Authors Eremko, A A, Brizhik, L S, Loktev, V M
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.12.2017
Subjects
Dirac equation
Operators
Particle spin
Physics - Mesoscale and Nanoscale Physics
Quantum wells
Relativism
Relativistic effects
Schrodinger equation
Spin-orbit interactions
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Summary:All relativistic corrections to the Scr{\"o}dinger 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1712.03161