Abstract
We apply Clifford algebra to investigate 2D electron spin reflection off and transmission through a stepped discontinuity of physical parameters in semiconducting quantum well. The discontinuity may be due to change of spin-orbit interaction constants, effective masses, or electrostatic potential. In the paper the posed problem has been solved exactly. It is shown that the reflected electronic beam has identical spin polarization as the incident one. However, the transmitted beam suffers spin flipping and in general case consists of a mixture of up and down spin states. Optimal conditions for total reversion of 2D electron spin polarization are found. Special attention is paid to correct boundary conditions in the presence of spin-orbit interaction. A simple formula that connects spin polarization of the transmitted beam and SO interaction constants is presented. Keywords: Clifford algebra, geometric algebra, semiconductors, spintronics, spin polarization, spin flipping, quantum well
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