TY  - JOUR
T1  - The existence and location of eigenvalues of the one particle Hamiltonians on lattices
AU  - Lakaev, Saidakhmat
AU  - Özdemir, Ender
PY  - 2016
DA  - December
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1693
EP  - 1703
VL  - 45
IS  - 6
LA  - en
AB  - We consider a quantum particle moving in the one dimensional latticeZ and interacting with a indefinite sign external field vˆ. We prove thatthe associated Hamiltonian H can have one or two eigenvalues, situatedas below the bottom of the essential spectrum, as well as above the itstop. Moreover, we show that the operator H can have two eigenvaluesoutside of the essential spectrum and one of them is situated below thebottom of the essential spectrum, and other one above its top
KW  - One particle Hamiltonian
KW  - essential spectrum
KW  - asymptotic
KW  - eigenvalue
CR  - .
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UR  - https://dergipark.org.tr/en/pub/hujms/issue//524289
L1  - https://dergipark.org.tr/en/download/article-file/644656
ER  -