Yu. P. Chuburin, “On small perturbations of the Schrödinger equation with periodic potential”, TMF, 110:3 (1997), 443–453; Theoret. and Math. Phys., 110:3 (1997), 351

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 110, Number 3, Pages 443–453
DOI: https://doi.org/10.4213/tmf980 (Mi tmf980)

This article is cited in 20 scientific papers (total in 20 papers)

On small perturbations of the Schrödinger equation with periodic potential

Yu. P. Chuburin

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Full-text PDF (247 kB) Citations (20)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf980

Abstract: We consider small perturbations of the potential periodic in variables

x_{j}

$x_j$ ,

$j=1,2,3$ , by a function wich is periodic in

$x_1$ ,

$x_2$ and exponentially decreases as

$|x_3|\to\infty$ . We prove that close to energies corresponding to the extrema in the third component of the quasy-momentum of nondegenerate eigenvalues of the Schrödinger operator with periodic potential considered in the cell there exists a unique (up to multiplicative factor) solution of the integral equation describing both eigenvalues and resonance levels. The asymptotic behaviour of the latter quantities is described.

Received: 14.10.1996

English version:
Theoretical and Mathematical Physics, 1997, Volume 110, Issue 3, Pages 351–359
DOI: https://doi.org/10.1007/BF02630460

Bibliographic databases:

Language: Russian

Citation: Yu. P. Chuburin, “On small perturbations of the Schrödinger equation with periodic potential”, TMF, 110:3 (1997), 443–453; Theoret. and Math. Phys., 110:3 (1997), 351–359

Citation in format AMSBIB

\Bibitem{Chu97}

\by Yu.~P.~Chuburin

\paper On small perturbations of the Schr\"odinger equation with periodic potential

\jour TMF

\yr 1997

\vol 110

\issue 3

\pages 443--453

\mathnet{http://mi.mathnet.ru/tmf980}

\crossref{https://doi.org/10.4213/tmf980}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1471189}

\zmath{https://zbmath.org/?q=an:0913.47013}

\transl

\jour Theoret. and Math. Phys.

\yr 1997

\vol 110

\issue 3

\pages 351--359

\crossref{https://doi.org/10.1007/BF02630460}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XU74600008}

Linking options:

https://www.mathnet.ru/eng/tmf980

https://doi.org/10.4213/tmf980

https://www.mathnet.ru/eng/tmf/v110/i3/p443

This publication is cited in the following 20 articles:

Yu. P. Chuburin, T. S. Tinyukova, “Behaviour of Andreev states for topological phase transition”, Theoret. and Math. Phys., 208:1 (2021), 977–992
Yu. P. Chuburin, T. S. Tinyukova, “Mutual transition of Andreev and Majorana bound states in a superconducting gap”, Theoret. and Math. Phys., 205:3 (2020), 1666–1681
T. S. Tinyukova, Yu. P. Chuburin, “Issledovanie sobstvennykh znachenii i rasseyaniya dlya gamiltoniana Bogolyubova–de Zhena vblizi granitsy sverkhprovodyaschei scheli”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:2 (2020), 259–269
Chuburin Yu.P., Tinyukova T.S., “The Emergence of Bound States in a Superconducting Gap At the Topological Insulator Edge”, Phys. Lett. A, 384:27 (2020), 126694
Yu. P. Chuburin, “Two-particle scattering in a periodic medium”, Theoret. and Math. Phys., 191:2 (2017), 738–751
T. S. Tinyukova, Yu. P. Chuburin, “Electron scattering by a crystal layer”, Theoret. and Math. Phys., 176:3 (2013), 1207–1219
T. S. Tinyukova, “Issledovanie raznostnogo uravneniya Shredingera dlya nekotorykh fizicheskikh modelei”, Izv. IMI UdGU, 2013, no. 2(42), 3–57
Yu. P. Chuburin, “Quasilevels of a two-particle Schrödinger operator with a perturbed periodic potential”, Theoret. and Math. Phys., 158:1 (2009), 96–104
Baranova, LY, “Quasi-levels of the two-particle discrete Schrodinger operator with a perturbed periodic potential”, Journal of Physics A-Mathematical and Theoretical, 41:43 (2008), 435205
L. E. Baranova, Yu. P. Chuburin, “Kvaziurovni dvukhchastichnogo diskretnogo operatora Shredingera s malym potentsialom”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 1, 35–46
Yu. P. Chuburin, “Decay law for a quasistationary state of the Schrödinger operator for a crystal film”, Theoret. and Math. Phys., 151:2 (2007), 648–658
Yu. P. Chuburin, “Perturbation Theory of Resonances and Embedded Eigenvalues of the Schrodinger Operator For a Crystal Film”, Theoret. and Math. Phys., 143:3 (2005), 836–847
Wolf, GV, “Specific features of low-energy electron scattering by thin films of cubic crystals”, Physics of the Solid State, 47:6 (2005), 1048
Chuburin, YP, “On levels of a weakly perturbed periodic Schrodinger operator”, Communications in Mathematical Physics, 249:3 (2004), 497
L. E. Morozova, Yu. P. Chuburin, “Ob urovnyakh odnomernogo diskretnogo operatora Shredingera s ubyvayuschim potentsialom”, Izv. IMI UdGU, 2004, no. 1(29), 85–94
N. I. Pletnikova, “Ob odnomernom uravnenii Shredingera s nelokalnym potentsialom tipa vozmuschennoi stupenki”, Izv. IMI UdGU, 2004, no. 1(29), 95–108
Yu. P. Chuburin, “Schrödinger operator eigenvalue (resonance) on a zone boundary”, Theoret. and Math. Phys., 126:2 (2001), 161–168
Yu. P. Chuburin, “Schrödinger operator with a perturbed small steplike potential”, Theoret. and Math. Phys., 120:2 (1999), 1045–1057
Yu. P. Chuburin, “Resonance multiplicity of a perturbed periodic Schrödinger operator”, Theoret. and Math. Phys., 116:1 (1998), 846–855
Vol'f, GV, “Resonance states of the continuous spectrum of a bounded crystal near the critical points of volume bands”, Physics of the Solid State, 40:11 (1998), 1813

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	582
Full-text PDF :	237
References:	99
First page:	1

Что такое QR-код?

Registration to the website

Logotypes