Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian

Details Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian Complete Set of Inner Products for a Discrete PT-symmetric Square-well Hamiltonian

2009-11-02

arxiv.org/abs/0911.0336v1

J. Math. Phys. 50, 122105 (2009)

Physics

Mathematical Physics

26 pp., 6 figures

Scientific paper

10.1063/1.3272002

A discrete $N-$point Runge-Kutta version $H^{(N)}({\lambda})$ of one of the simplest non-Hermitian square-well Hamiltonians with real spectrum is studied. A complete set of its possible hermitizations (i.e., of the eligible metrics $\Theta^{(N)}({\lambda})$ defining its non-equivalent physical Hilbert spaces of states) is constructed, in closed form, for any coupling ${\lambda}\in (-1,1)$ and any matrix dimension $N$.

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