Abstract
The motion of particles in potentials which become minus infinity at some point has been investigated. It is shown that the state localized at the point of the potential drop is the ground state of the particle; for excited states, whose wave functions do not vanish at the point where the potential drops, the fairly abrupt potential drop is equivalent to the existence of a potential barrier at that point.
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Yu. N. Demkov and V. N. Ostrovskii, Method of Zero-Radius Potentials in Atomic Physics [in Russian], Leningrad (1975).
S. Flügge, Practical Quantum Mechanics, 2 Vols. Springer-Verlag, Berlin (1971).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Nonrelativistic Theory, Pergamon Press, Oxford (1965).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 102–106, July, 1982.
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Nurmagambetov, S.B. Influence of an abrupt drop in potential on particle motion. Soviet Physics Journal 25, 676–680 (1982). https://doi.org/10.1007/BF00911806
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DOI: https://doi.org/10.1007/BF00911806