Research Article

The existence and location of eigenvalues of the one particle Hamiltonians on lattices

Volume: 45 Number: 6 December 1, 2016
  • Saidakhmat Lakaev *
  • Ender Özdemir
EN

The existence and location of eigenvalues of the one particle Hamiltonians on lattices

Abstract

We consider a quantum particle moving in the one dimensional lattice Z and interacting with a indefinite sign external field vˆ. We prove that the associated Hamiltonian H can have one or two eigenvalues, situated as below the bottom of the essential spectrum, as well as above the its top. Moreover, we show that the operator H can have two eigenvalues outside of the essential spectrum and one of them is situated below the bottom of the essential spectrum, and other one above its top

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Saidakhmat Lakaev * This is me

Ender Özdemir This is me

Publication Date

December 1, 2016

Submission Date

September 29, 2015

Acceptance Date

January 28, 2016

Published in Issue

Year 2016 Volume: 45 Number: 6

APA
Lakaev, S., & Özdemir, E. (2016). The existence and location of eigenvalues of the one particle Hamiltonians on lattices. Hacettepe Journal of Mathematics and Statistics, 45(6), 1693-1703. https://izlik.org/JA57AF29RP
AMA
1.Lakaev S, Özdemir E. The existence and location of eigenvalues of the one particle Hamiltonians on lattices. Hacettepe Journal of Mathematics and Statistics. 2016;45(6):1693-1703. https://izlik.org/JA57AF29RP
Chicago
Lakaev, Saidakhmat, and Ender Özdemir. 2016. “The Existence and Location of Eigenvalues of the One Particle Hamiltonians on Lattices”. Hacettepe Journal of Mathematics and Statistics 45 (6): 1693-1703. https://izlik.org/JA57AF29RP.
EndNote
Lakaev S, Özdemir E (December 1, 2016) The existence and location of eigenvalues of the one particle Hamiltonians on lattices. Hacettepe Journal of Mathematics and Statistics 45 6 1693–1703.
IEEE
[1]S. Lakaev and E. Özdemir, “The existence and location of eigenvalues of the one particle Hamiltonians on lattices”, Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 6, pp. 1693–1703, Dec. 2016, [Online]. Available: https://izlik.org/JA57AF29RP
ISNAD
Lakaev, Saidakhmat - Özdemir, Ender. “The Existence and Location of Eigenvalues of the One Particle Hamiltonians on Lattices”. Hacettepe Journal of Mathematics and Statistics 45/6 (December 1, 2016): 1693-1703. https://izlik.org/JA57AF29RP.
JAMA
1.Lakaev S, Özdemir E. The existence and location of eigenvalues of the one particle Hamiltonians on lattices. Hacettepe Journal of Mathematics and Statistics. 2016;45:1693–1703.
MLA
Lakaev, Saidakhmat, and Ender Özdemir. “The Existence and Location of Eigenvalues of the One Particle Hamiltonians on Lattices”. Hacettepe Journal of Mathematics and Statistics, vol. 45, no. 6, Dec. 2016, pp. 1693-0, https://izlik.org/JA57AF29RP.
Vancouver
1.Saidakhmat Lakaev, Ender Özdemir. The existence and location of eigenvalues of the one particle Hamiltonians on lattices. Hacettepe Journal of Mathematics and Statistics [Internet]. 2016 Dec. 1;45(6):1693-70. Available from: https://izlik.org/JA57AF29RP