Geodesic
Solutions of one-dimensional Schrödinger equation with hardy-type potential. The $S$-matrix formalism
Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 3, pp. 380-387 Cet article a éte moissonné depuis la source Math-Net.Ru

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A general method is developed for investigating the solutions of the scattering problem for the one-dimensional SchrSdinger equation with Hardy potential. The method uses the formalism of stationary scattering theory. In the quasiclassical and wave (anticlassical) approximations, calculations are made of the amplitude of reflection of particles from a potential with Hardy function describing Bragg scattering of shortwavelength radiation on static elastic distortions of dislocation type in a crystal lattice. 
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     title = {Solutions of one-dimensional {Schr\"odinger} equation with hardy-type potential. {The} $S$-matrix formalism},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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A. M. Arustamyan; V. L. Vergasov; F. N. Chukhovskii. Solutions of one-dimensional Schrödinger equation with hardy-type potential. The $S$-matrix formalism. Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 3, pp. 380-387. http://geodesic.mathdoc.fr/item/TMF_1979_38_3_a9/

[1] V. L. Pokrovskii, I. M. Khalatnikov, ZhETF, 40 (1961), 1713

[2] A. Z. Patashinskii, V. L. Pokrovskii, I. M. Khalatnikov, ZhETF, 44 (1963), 2062 | MR

[3] A. Z. Patashinskii, V. L. Pokrovskii, I. M. Khalatnikov, ZhETF, 45 (1963), 760 | MR

[4] A. Z. Patashinskii, V. L. Pokrovskii, I. M. Khalatnikov, ZhETF, 45 (1963), 989 | MR

[5] F. N. Chukhovskii, A. A. Shtolberg, ZhETF, 64 (1973), 1033

[6] P. V. Petrashen, F. N. Chukhovskii, ZhETF, 69 (1975), 477

[7] G. Dzheffris, B. Svirls, Metody matematicheskoi fiziki, t. 3, «Mir», 1970 | MR

[8] Dzh. Kheding, Vvedenie v metod fazovykh integralov (metod VKB), «Mir», 1965, str. 43

[9] N. Freman, P. U. Freman, VKB-priblizhenie, «Mir», 1967, str. 122

[10] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Fizmatgiz, 1963

[11] V. A. Kolkunov, TMF, 2 (1970), 169

[12] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. 1, «Nauka», 1965 | MR