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This article is cited in 9 scientific papers (total in 9 papers)
Perturbation theory formulas for the Schrödinger equation with a nonsmooth periodic potential
Yu. E. Karpeshina Leningrad State University
Abstract:
Series from perturbation theory are constructed for the Bloch eigenvalues and eigenfunctions for the periodic Schrödinger operator in $R^3$. An extensive set of quasimomenta on which the series converge is described. It is shown that the series have asymptotic character at high energies. They are infinitely differentiable with respect to the quasimomentum, and preserve their asymptotic character under such differentiation.
Received: 09.01.1990
Citation:
Yu. E. Karpeshina, “Perturbation theory formulas for the Schrödinger equation with a nonsmooth periodic potential”, Mat. Sb., 181:9 (1990), 1256–1278; Math. USSR-Sb., 71:1 (1992), 101–123
Linking options:
https://www.mathnet.ru/eng/sm1224https://doi.org/10.1070/SM1992v071n01ABEH002127 https://www.mathnet.ru/eng/sm/v181/i9/p1256
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Abstract page: | 270 | Russian version PDF: | 129 | English version PDF: | 6 | References: | 37 | First page: | 1 |
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