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Solvable non-Hermitian discrete square well with closed-form physical inner product

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    0436875 - ÚJF 2015 RIV GB eng J - Journal Article
    Znojil, Miloslav
    Solvable non-Hermitian discrete square well with closed-form physical inner product.
    Journal of Physics A-Mathematical and Theoretical. Roč. 47, č. 43 (2014), s. 435302. ISSN 1751-8113. E-ISSN 1751-8121
    Institutional support: RVO:61389005
    Keywords : exactly sovable quantum models * discrete lattice * non-Hermitian boundary conditions * physical inner product
    Subject RIV: BE - Theoretical Physics
    Impact factor: 1.583, year: 2014

    A new Hermitizable quantum model is proposed in which the bound-state energies are real and given as roots of an elementary trigonometric expression while the wave function components are expressed as superpositions of two Chebyshev polynomials. As an N-site lattice version of square well with complex Robin-type two-parametric boundary conditions the model is unitary with respect to the Hilbert space metric T which becomes equal to the most common Dirac's metric Theta((Dirac)) = I in the conventional textbook Hermitian-Hamiltonian limit. This metric is constructed in closed form at all N = 2, 3, ....
    Permanent Link: http://hdl.handle.net/11104/0240518

     
     
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