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2005 | 3 | 4 | 591-609
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Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

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We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

Opis fizyczny
  • Department of Mathematics, Swiss Federal Institute of Technology Zürich (ETH), ETH-Zentrum HG E 18.4, CH-8092, Zürich, Switzerland,
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