Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation

Details Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation

2010-12-04

arxiv.org/abs/1012.0907v1

Int.J.Theor.Phys.50:1143-1151,2011

Physics

Quantum Physics

To appear in the Special Issue PHHQP 2010, International Journal of Theoretical Physics; 16 pages, LateX, no figure

Scientific paper

10.1007/s10773-010-0618-5

A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ spin-chain are considered.

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