2007/10/31 by Miloslav Znojil · 1 citation
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:46C20 #msc:47B50 #msc:81P10 #msc:81R05 #quant-ph
paper · pdf · doi:10.3842/sigma.2008.001
published as SIGMA 4 (2008), 001, 9 pages · This is a contribution to the Proc. of the 3-rd Microconference "Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2008/01/02 · openalex publication_date 2008/01/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Among P-pseudo-Hermitian Hamiltonians H = P -1 H P with real spectra, the "weakly pseudo-Hermitian" ones (i.e., those employing non-self-adjoint P = P ) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P = P , the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity operator Q. We show how, in this language, the standard quantum mechanics is restored via the two alternative inner products in the physical Hilbert space of states, with