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Author Joglekar, Yogesh N.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ♦ ATOMIC AND MOLECULAR PHYSICS ♦ EIGENFUNCTIONS ♦ EIGENVALUES ♦ ENERGY LEVELS ♦ HAMILTONIANS ♦ MAPPING ♦ PARITY ♦ POTENTIALS ♦ QUANTUM STATES ♦ SYMMETRY ♦ FUNCTIONS ♦ MATHEMATICAL OPERATORS ♦ PARTICLE PROPERTIES ♦ QUANTUM OPERATORS
Abstract Through a simple and exact analytical derivation, we show that for a particle on a lattice there is a one-to-one correspondence between the spectrum in the presence of an attractive potential V and its repulsive counterpart -V. For a Hermitian potential, this result implies that the number of localized states is the same in both attractive and repulsive cases although these states occur above (below) the band continuum for the repulsive (attractive) case. For a PT-symmetric potential that is odd under parity, our result implies that, in the PT-unbroken phase, the energy eigenvalues are symmetric around zero and that the corresponding eigenfunctions are closely related to each other.
ISSN 10502947
Educational Use Research
Learning Resource Type Article
Publisher Date 2010-10-15
Publisher Place United States
Journal Physical Review. A
Volume Number 82
Issue Number 4


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