Geodesic
Discrete symmetry in quantum scattering
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 60-79 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the discrete symmetries of the Klein–Gordon, Dirac, and Schrödinger wave equations, we obtain from one solution, considered as a function of the quantum numbers and the parameters of the potentials, three other solution. Taken together, these solutions form two complete sets of solutions of the wave equation. The coefficients of the linear relations between the functions of these sets – the connection coefficients – are related in a simple manner to the wave transmission and reflection amplitudes. By virtue of the discrete symmetries of the wave equation, the connection coefficients satisfy certain symmetry relations. We show that in a number of simple cases, the behavior of the wave function near the center of formation of an additional wave determines the amplitude of the wave that is formed at infinity. 
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A. I. Nikishov. Discrete symmetry in quantum scattering. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 60-79. http://geodesic.mathdoc.fr/item/TMF_1994_98_1_a6/

[1] Willard Miller, Jr., Symmetry and Separation of Variables, Addison-Wesley, 1977 | MR | Zbl

[2] Malkin I. A., Manko V. I., Dinamicheskie simmetrii i kogerentnye sostoyaniya kvantovykh sistem, Nauka, M., 1979 | MR

[3] Fuschich V. I., Nikitin A. G., Simmetriya uravnenii kvantovoi mekhaniki, Nauka, M., 1990 | MR

[4] Nikishov A. I., Tr. FIAN, 111 (1979)

[5] Grib A. A., Mamaev S. G., Mostepanenko V. M., Vakuumnye kvantovye effekty v silnykh polyakh, Energoizdat, M., 1988

[6] Landau L. D., Lifshits E. M., Kvantovaya mekhanika, Nauka, M., 1989 | MR

[7] Akhiezer A. I., Berestetskii V. B., Kvantovaya elektrodinamika, Nauka, M., 1969 | MR

[8] Messia A., Kvantovaya mekhanika, T. 2, Mir, M., 1978 | MR

[9] Nikishov A. I., YaF, 46 (1987), 163

[10] Flyugge Z., Zadachi po kvantovoi mekhanike, Mir, M., 1974

[11] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

[12] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, T. II, GIFML, M., 1963

[13] Lyuk Yu., Spetsialnye matematicheskie funktsii i ikh approksimatsii, Mir, M., 1980

[14] Miller J. C. P., Tables of Weber Parabolic Cylinder Function, Her Majesty's Stationery Office, London, 1955 | MR | Zbl

[15] Berry M. V., Proc. Roy. Soc. Lond., A422:1862 (1989), 7 | DOI | MR

[16] Nikishov A. I., Ritus V. I., TMF, 92:1 (1992), 24–40 | MR

[17] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. I, Nauka, M., 1968 | MR