Ma'lumot

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

Sh. I. Khamidov


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.



https://doi.org/10.59251/2181-1296.v5.1292.833

Sahifalar soni 01-13 | 150 Ko'rishlar | 115 Yuklab olishlar

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