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IKKI O‘LCHAMLI PANJARADAGI SISTEMALARGA MOS DISKRET SHREDINGER OPERATORLARI XOS QIYMATLARI VA ULARNING ASIMPTOTIKALARI

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MAQOLA ANNOTATSIYASI

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Biz ikki o‘lchamli panjarada Hvμ- bir zarrachali diskret Schrödinger operatorini o‘rganamiz. Hvμ operatorning muhim spektrdan yuqorida xos qiymatlari mavjudligi yoki mavjud emasligini va sonini aniqlaymiz. Bundan tashqari, xos qiymat funksiyasining xossalarini va yetarlicha kichik, musbat μ larda xos qiymatning asimptotikasini o‘rganamiz

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# оператор# xos qiymat# собственное значение# eigenvalue# спектр# spectrum# operator# асимптотика# spektr# xos qiymat asimptotikasi# eigenvalue asymptotic

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Foydalanilgan adabiyotlar

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[7] S.N. Lakaev, Sh.Yu. Kholmatov: Asymptotics of eigenvalues of two-particle Schrodinger operators on lattice¨s with zero-range interaction.J. Phys. A: Math. Theor. 44 (2011)

[8] Shokhrukh Yu. Kholmatov, Saidakhmat N. Lakaev, Firdavsjon M. Almuratov: On the spectrum of Schrödinger-type operators on two dimensional lattices, Journal of Mathematical Analysis and Applications, 514(2) (2022), 126363. https://doi.org/10.1016/j.jmaa.2022.126363

[9] Lakaev, S.N., Boltaev, A.T. & Almuratov, F.M. On The Discrete Spectra of Schrödinger-Type Operators on one Dimensional Lattices. Lobachevskii J Math 43, 770–783 (2022).https://doi.org/10.1134/S199508022206018X

[10] M. Reed, B. Simon: Modern Methods of Mathematical Physics. IV: Analysis of Operators. Academic Press, New York. (1978).

[11] B. Simon: The bound state of weakly coupled Schrodinger operators in one and two dimension¨s.Ann. Phys. 97 (1976), 279–288

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