author={Bijan Bagchi and Sadek Hossain Mallik and C Quesne},
  journal={Modern Physics Letters A},
The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength Z lies below the critical value where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of sec2-like potentials in the Z → 0 limit. For Z above , there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration. 

SUSY Quantum Mechanics for PT Symmetric Systems

A new way of constructing SUSY partner potentials with PT symmetry is proposed. In this construction, PT symmetric superpotentials generate PT symmetric SUSY partners and supercharges that satisfy

Exact Analytic Study of the PT-Symmetry-Breaking Mechanism

We employ the exactly solvable Scarf II potential to illustrate how the spontaneous breakdown of PT symmetry is realized, and how it influences the discrete energy spectrum, the solutions and their

Fragile PT-symmetry in a solvable model

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

Solvability and PT-symmetry in a double-well model with point interactions

The concept of point interactions offers one of the most suitable guides towards a quantitative analysis of properties of certain specific non-Hermitian (so-called -symmetric) quantum-mechanical

Coupled-channel version of the PT-symmetric square well

A coupled pair of PT-symmetric square wells is studied as a prototype of a quantum system characterized by two manifestly non-Hermitian commuting observables. Via the diagonalization of our

Exactly solvable models with -symmetry and with an asymmetric coupling of channels

Bound states generated by the K coupled -symmetric square wells are studied in a series of models where the Hamiltonians are assumed -pseudo-Hermitian and -symmetric. Specific rotation-like


The simplest purely imaginary and piecewise constant -symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound

symmetric regularizations in supersymmetric quantum mechanics

Within supersymmetric quantum mechanics the necessary regularization of the poles of the superpotentials on the real line of coordinates x may be most easily mediated by a small constant shift of

Supersymmetric Solutions of PT-/non-PT-symmetric and Non-Hermitian Central Potentials via Hamiltonian Hierarchy Method

The supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian deformed Morse and Pöschl-Teller potentials are obtained by solving the Schrödinger equation. The Hamiltonian hierarchy method

Calculation of the hidden symmetry operator for a -symmetric square well

It has been shown that a Hamiltonian with an unbroken symmetry also possesses a hidden symmetry that is represented by the linear operator . This symmetry operator guarantees that the Hamiltonian



SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra

We extend the standard intertwining relations used in supersymmetrical (SUSY) quantum mechanics which involve real superpotentials to complex superpotentials. This allows us to deal with a large

Generating complex potentials with real eigenvalues in supersymmetric quantum mechanics

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based

Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry

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 $\mathrm{PT}$ symmetry, one obtains new

The Interpretation of Quantum-Mechanical Models with Non-Hermitian Hamiltonians and Real Spectra

We study the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. We set up a general framework for the analysis of such systems in terms of Hermitian

Generalized continuity equation and modified normalization in PT-symmetric quantum mechanics

The continuity, equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The

Higher Transcendental Functions

Higher Transcendental FunctionsBased, in part, on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project. Vol. 1. Pp. xxvi + 302. 52s. Vol. 2. Pp. xvii + 396.


  • Lett. A285, 7
  • 2001