Abstract
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.
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Schulze-Halberg, A. Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions. centr.eur.j.phys. 3, 591–609 (2005). https://doi.org/10.2478/BF02475615
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DOI: https://doi.org/10.2478/BF02475615