Threshold effects in the spectrum of the one-particle schrödinger operator on a lattice

S N Lakaev, S h I Khamidov

Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi · 2020-yil

Annotatsiya

We consider a wide class of Schrödinger operators HV = H0 V describing a particle in an external force field vˆ in the d -dimensional cubic integer lattice d , d  3 . We study the existence or absence of bound states of the one-particle Schrödinger operator HV depending on the potential vˆ and the dimension of the lattice d , d  3, as well as threshold effects in its spectrum. We establish that the appearance of bound states of the operator HV depends on whether the threshold of the essential spectrum of HV is a regular point or a singular point: namely, if the lower threshold of the essential spectrum of HV is a regular point of the essential spectrum, then it does not create any eigenvalues below the essential spectrum under small perturbations, but if the lower threshold of the essential spectrum of the operator HV is a singular point, then it creates eigenvalues below the essential spectrum under perturbations.

Maqola ma’lumotlari
MualliflarS N Lakaev, S h I Khamidov
JurnalSamarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi
NashriyotСамарқанд давлат университети
ISSN2091-5446, 2181-1296
Nashr sanasi2020-06-03
Jild5
Son123/1
Betlar1-17
TilIngliz
Ilmiy sohaKimyo
DOI10.59251/2181-1296.v5.1231.1416
Indeksga qo‘shilgan2026-09-02

DOI: 10.59251/2181-1296.v5.1231.1416 · Maqolaning asl sahifasi

Ilmiy soha

Kimyo

Iqtibos keltirish

APAS N Lakaev, & S h I Khamidov (2020). THRESHOLD EFFECTS IN THE SPECTRUM OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(123/1), 1-17. https://doi.org/10.59251/2181-1296.v5.1231.1416
GOST (OAK)S N Lakaev, S h I Khamidov THRESHOLD EFFECTS IN THE SPECTRUM OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2020. – T. 5, № 123/1. – P. 1-17. – DOI: 10.59251/2181-1296.v5.1231.1416.
MLAS N Lakaev, and S h I Khamidov. “THRESHOLD EFFECTS IN THE SPECTRUM OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(123/1), 1-17, 2020. https://doi.org/10.59251/2181-1296.v5.1231.1416
ChicagoS N Lakaev, and S h I Khamidov. “THRESHOLD EFFECTS IN THE SPECTRUM OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(123/1), 1-17 (2020). https://doi.org/10.59251/2181-1296.v5.1231.1416
HarvardS N Lakaev, and S h I Khamidov (2020) ‘THRESHOLD EFFECTS IN THE SPECTRUM OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 5(123/1), 1-17. https://doi.org/10.59251/2181-1296.v5.1231.1416
BibTeX
@article{snlakaev2020,
  title = {THRESHOLD EFFECTS IN THE SPECTRUM OF THE ONE-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE},
  author = {S N Lakaev and S h I Khamidov},
  journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
  year = {2020},
  volume = {5},
  number = {123/1},
  pages = {1-17},
  doi = {10.59251/2181-1296.v5.1231.1416},
  url = {https://doi.org/10.59251/2181-1296.v5.1231.1416}
}

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