Related papers: PT-symmetric supersymmetry in a solvable short-ran…
In a box of size $L$, a spatially antisymmetric square-well potential of a purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of which are…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
SUSY partnership between singular potentials often breaks down. Via regularization it can be restored on certain ad hoc subspaces of Hilbert space [Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally complexified (so called…
Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly…
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
A conditionally exactly solvable potential, the supersymmetric partner of the harmonic oscillator is investigated in the PT-symmetric setting. It is shown that a number of properties characterizing shape-invariant and Natanzon-class…
We extend the standard intertwining relations used in Supersymmetrical (SUSY) Quantum Mechanics which involve real superpotentials to complex superpotentials. This allows to deal with a large class of non-hermitean Hamiltonians and to study…
Supersymmetry offers one of the deepest insights in the concept of solvability in quantum mechanics. This insight is, paradoxically, restricted by one of the most serious formal drawbacks of the standard Witten's formulation of…
We introduce and study a class of non-Hermitian Hamiltonians which have velocity dependent potentials. Since stability can not be advocated directly from the classical potential, we show that the energy spectra are real and bounded from…
The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the…
Within the framework of the recently proposed formalism using non-hermitean Hamiltonians constrained merely by their PT invariance we describe a new exactly solvable family of the harmonic-oscillator-like potentials with non-equidistant…
We construct an isospectrum systems in terms of a real and complex potential to show that the underlying PT symmetric Hamiltonian possesses a real spectrum which is shared by its real partner.
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are…
The Hilbert space in PT-symmetric quantum mechanics is formulated as a linear vector space with a dynamic inner product. The most general PT-symmetric matrix Hamiltonians are constructed for 2*2 and 3*3 cases. In the former case, the…
One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to…
We show that the PT symmetric Hamiltonians (and their generalizations defined in the text) may be all assigned the projected (so called Feshbach or effective) nonlinear Hamiltonians which are "locally" Hermitian. This implies that many (if…
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians…
The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that…
One-dimensional PT-symmetric quantum-mechanical Hamiltonians having continuous spectra are studied. The Hamiltonians considered have the form $H=p^2+V(x)$, where $V(x)$ is odd in $x$, pure imaginary, and vanishes as $|x|\to\infty$. Five…