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

0436875 - ÚJF 2015 RIV GB eng J - Článek v odborném periodiku
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
Institucionální podpora: RVO:61389005
Klíčová slova: exactly sovable quantum models * discrete lattice * non-Hermitian boundary conditions * physical inner product
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.583, rok: 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, ....
Trvalý link: http://hdl.handle.net/11104/0240518