Abstract
The quantum mechanical problem of a single electron-hole pair in a homogeneous semiconductor leads to the Wannier equation, which, for a parabolic bandstructure is mathematically identical to the hydrogen atom Schrödinger equation [1]. This equation can be solved analytically in three and two dimensions, which is relevant for idealized bulk or quantum-well structures. Solutions are also available for quasi-one dimensional systems, however, their treatment requires the regularization of the Coulomb interaction potential [2, 3].
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Koch, S.W., Kira, M. (2004). Excitons in Semiconductors. In: Kalt, H., Hetterich, M. (eds) Optics of Semiconductors and Their Nanostructures. Springer Series in Solid-State Sciences, vol 146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09115-9_1
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DOI: https://doi.org/10.1007/978-3-662-09115-9_1
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