Abstract:
For the equation −ψ″+p(x)ψ+q(εx)ψ=0, p – periodic function, ε→0), behaviour
of solutions in neighbourhood of two close turning points is studied. The results give
mathematically consistent description of the electric breakdown effect in the Block
electron theory.
Citation:
V. S. Buslaev, L. A. Dmitrieva, “Adiabatic perturbation of periodic potential. II”, TMF, 73:3 (1987), 430–442; Theoret. and Math. Phys., 73:3 (1987), 1320–1329
This publication is cited in the following 14 articles:
S. Yu. Dobrokhotov, “Asymptotics of the Cauchy Problem for the One-Dimensional Schrödinger Equation with Rapidly Oscillating Initial Data and Small Addition to the Smooth Potential”, Russ. J. Math. Phys., 30:4 (2023), 466
A. R. Bikmetov, I. Kh. Khusnullin, “Perturbation of Hill operator by narrow potentials”, Russian Math. (Iz. VUZ), 61:7 (2017), 1–10
V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, St. Petersburg Math. J., 25:2 (2014), 151–174
A. A. Fedotov, “Monodromization method in the theory of almost-periodic equations”, St. Petersburg Math. J., 25:2 (2014), 303–325
Glebov, S, “Weakly Nonlinear Dispersive Waves under Parametric Resonance Perturbation”, Studies in Applied Mathematics, 124:1 (2010), 19
A. A. Fedotov, “Complex WKB method for adiabatic perturbations of a periodic Schrödinger operator”, J. Math. Sci. (N. Y.), 173:3 (2011), 320–339
A. A. Pozharskii, “Semicrystal with a singular potential in an accelerating electric field”, Theoret. and Math. Phys., 146:3 (2006), 343–360
A. A. Pozharskii, “On the nature of the Stark–Wannier spectrum”, St. Petersburg Math. J., 16:3 (2005), 561–581
A. A. Pozharskii, “A crystal with a singular potential in a homogeneous electric field”, Theoret. and Math. Phys., 123:1 (2000), 524–538
M.V. Perel, I.V. Fialkovsky, A.P. Kiaelev, International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450), 2000, 118
V. S. Buslaev, Recent Developments in Quantum Mechanics, 1991, 97
J.-M. Combes, P. D. Hislop, “Stark ladder resonances for small electric fields”, Commun.Math. Phys., 140:2 (1991), 291
V. S. Buslaev, Order,Disorder and Chaos in Quantum Systems, 1990, 85
M. V. Perel', “Overexcitation of modes in an anisotropic earth-ionosphere waveguide on transequatorial paths in the presence of two close degeneracy points”, Radiophys Quantum Electron, 33:11 (1990), 882
Citation in format AMSBIB
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