Geodesic
Levels of the Schrödinger operator with a perturbed non-local potential
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 1 (2006), pp. 98-104 
M. S. Smetanina. Levels of the Schrödinger operator with a perturbed non-local potential. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 1 (2006), pp. 98-104. http://geodesic.mathdoc.fr/item/IIMI_2006_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the one-dimensional Schrödinger operator with a potential that is a sum of a local potential and a two-rank operator. We prove that this Schrödinger operator has the unique level in the neighborhood of zero. The asimptotic behaviour of this level is investigated.

[1] Kheine V., Koen M., Ueir D., Teoriya psevdopotentsiala, Mir, M., 1973, 560 pp.

[2] Smetanina M. S., “Ob uravnenii Shredingera s nelokalnym potentsialom”, Izvestiya In-ta matem. i inform. UdGU. Izhevsk, 2002, no. 3 (26), 99–114

[3] Smetanina M. S., “Asimptotika urovnei odnomernogo operatora Shredingera s nelokalnym potentsialom”, Izvestiya In-ta matem. i inform. UdGU. Izhevsk, 2005, no. 1 (31), 99–106

[4] Albeverio S., Gestezi F., Kheeg-Kron R., Kholden Kh., Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991, 568 pp. | MR