Treating some solid state problems with the Dirac equation

Details Treating some solid state problems with the Dirac equation Treating some solid state problems with the Dirac equation

1999-11-22

arxiv.org/abs/cond-mat/9911356v1

J.Phys. A33 (2000) L509

Physics

Condensed Matter

06 pages, 5 figures

Scientific paper

10.1088/0305-4470/33/50/103

The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary potential and effective-mass profiles without ordering problems. On the other hand, if the Schrodinger equation is supposed to be used, our relativistic approach demonstrate that both results are coincidents if the BenDaniel and Duke prescription for the kinetic-energy operator is implemented. Applications for semiconductor heterostructures are discussed.

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