THE EXISTENCE OF EIGENVALUES OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE

S h I Khamidov

Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi · 2021-yil

Annotatsiya

We consider a wide class of Schrödinger operators H H V V = 0  describing a particle in an external force field v ˆ in the d -dimensional cubic integer lattice , 3 d d  . We study the existence or absence of bound states of the one-particle Schrödinger operator HV depending on the potential v ˆ and the dimension of the lattice , 3 d d  . We obtain some sufficient conditions for the existence of eigenvalues of the operator HV lying below the essential spectrum.

Maqola ma’lumotlari
MualliflarS h I Khamidov
JurnalSamarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi
Nashr sanasi2021-06-19
Jild5
Son129/2
Betlar1-13
Tilen
DOI10.59251/2181-1296.v5.1292.833

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