Abstract
In this paper, an apparently universal feature of the ground-state energy of a particle in a potential well is pointed out. Namely, by the example of an infinitely deep rectangular potential well, we clearly demonstrate that this energy, as well as the localization energy of a particle ensuing from the Heisenberg relation, is accumulated by the work of an external force against the particle pressure force on the well walls during compression of the particle substance and, correspondingly, its wave function ψ from unbounded free space to the finite volume of the well. This work is exactly equal to the particle ground-state energy.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, Nos. 10–11, pp. 925–927, October–November, 2004.
This work was partially supported by CRDF and the Ministry of Education of the Russian Federation (grant VZ-010-0).
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Rivlin, L.A. Origin of the ground-state energy of a particle in a potential well. Radiophys Quantum Electron 47, 832–834 (2004). https://doi.org/10.1007/s11141-005-0022-9
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DOI: https://doi.org/10.1007/s11141-005-0022-9