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Quantum mechanics with coordinate-dependent mass

A. V. Kolesnikov·A. P. Silin
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Abstract

We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed between two semiconductors. We predict a new type of electron states, localized at the interface. They appear whenever the two bulk dispersions intersect. These shallow states lie near the point of intersection and are restricted to a finite range of perpendicular momentum. The scattering of carriers by the interface is discussed.

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A. V. Kolesnikov, A. P. Silin. 1998-10-26. Quantum mechanics with coordinate-dependent mass. https://doi.org/10.1103/physrevb.59.7596

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