Geodesic
Generation of new exactly solvable potentials of a nonstationary Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 3, pp. 426-433 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method for generating integrable potentials of a nonstationary Schrödinger equation (i.e., with time-dependent potential) is developed on the basis of the method of “dressing” of linear differential operators. Potentials that admit separation of the variables generate classes of nonseparating potentials for which the Schrödinger equation has nonlocal symmetry operators. 
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     author = {V. G. Bagrov and A. V. Shapovalov and I. V. Shirokov},
     title = {Generation of new exactly solvable potentials of a~nonstationary {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1991_87_3_a6/}
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V. G. Bagrov; A. V. Shapovalov; I. V. Shirokov. Generation of new exactly solvable potentials of a nonstationary Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 87 (1991) no. 3, pp. 426-433. http://geodesic.mathdoc.fr/item/TMF_1991_87_3_a6/

[1] Marchenko V. A., Operatory Shturma-Liuvilya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR

[2] Levitan B. M., Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[3] Zakharov V. E., Shabat A. B., Funkts. analiz i ego prilozh., 8:3 (1974), 43–53 | MR | Zbl

[4] Zakharov V. E., “Metod obratnoi zadachi rasseyaniya”, Solitony, eds. Bullaf R., Kodri F., Mir, M., 1983, 270–309

[5] Shapovalov V. N., Differents. uravneniya, 16:10 (1980), 1864–1874 | MR | Zbl

[6] Konopelchenko B. G., Mokhnachev V. G., YaF, 30:2 (1979), 559–567 | MR | Zbl

[7] Kaptsov O. V., DAN SSSR, 262:5 (1982), 1056–1059 | MR | Zbl

[8] Akhatov I. Sh., Gazizov R. K., Ibragimov N. X., Itogi nauki i tekhniki. Sovrem. probl. matematiki. Noveishie dostizheniya, 34, VINITI, M., 1989, 3–83 | MR

[9] Fuschich V. I., Nikitin A. G., EChAYa, 14:1 (1983), 5–57 | MR

[10] Bagrov V. G., Gitman D. M., Ternov I. M. i dr., Tochnye resheniya relyativistskikh volnovykh uravnenii, Nauka, Novosibirsk, 1982

[11] Abraham P. B., Moses H. E., Phys. Rev. A, 22:4 (1980), 1333–1340 | DOI | MR

[12] Pursey D. L., Phys. Rev. D, 33:4 (1986), 1048–1055 | DOI | MR

[13] Pursey D. L., Phys. Rev. D, 36:4 (1987), 1103–1118 | DOI | MR

[14] Bagrov V. G., Shapovalov A. V., Shirokov I. V., Izv. vuzov. Fizika, 1989, no. 11, 114–116 | MR

[15] Bagrov V. G., Shapovalov A. V., Shirokov I. V., Phys. Lett. A, 147:7 (1990), 348–350 | DOI | MR

[16] Shapovalov V. N., Sukhomlin N. B., Izv. vuzov. Fizika, 1974, no. 12, 100–105

[17] Schrödinger E., Naturwissenschaften, 14:28 (1926), 664–666 | DOI | Zbl

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