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Crypto-Hermiticity; Sturm–Schrödinger bound-state problem.

Sturm–Schrödinger equations $H\psi = EW\psi$ with $H \neq H^{\dagger}$ and $W \neq W^{\dagger} \neq I$ are considered, with a weak point of the theory lying in the purely numerical matrix- inversion form of the double-series definition of the necessary metric operator 𝛩 in the physical Hilbert space of states [M Znojil, J. Phys. A: Math. Theor. 41, 215304 (2008)]. This shortcoming is removed here via an amended, single-series definition of 𝛩.

Miloslav Znojil¹ Hendrik B Geyer²

1. Nuclear Physics Institute ASCR, 250 68 Řež, Czech Republic
2. Institute of Theoretical Physics, University of Stellenbosch and Stellenbosch Institute for Advanced Study, 7600 Stellenbosch, South Africa

Published

August 2009