Abstract
The Bloch states of a particle in a one-dimensional, periodic, biparabolic field are determined. The solutions are expressed in terms of confluent hypergeometric functions. It is shown that the first term of the Tricomi expansion for confluent hypergeometric functions represents the quasifree above-barrier motion of a particle and is identical to the exact Kronig-Penney solution for a square potential.
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References
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Fiz. Tverd. Tela (St. Petersburg) 41, 1317–1319 (July 1999)
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Muradyan, A.Z. Kronig-Penney problem for a biparabolic potential: Quasifree particle motion. Phys. Solid State 41, 1204–1206 (1999). https://doi.org/10.1134/1.1130967
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DOI: https://doi.org/10.1134/1.1130967