# PT-SYMMETRIC SQUARE WELL AND THE ASSOCIATED SUSY HIERARCHIES

@article{Bagchi2002PTSYMMETRICSW, title={PT-SYMMETRIC SQUARE WELL AND THE ASSOCIATED SUSY HIERARCHIES}, author={Bijan Bagchi and Sadek Hossain Mallik and C Quesne}, journal={Modern Physics Letters A}, year={2002}, volume={17}, pages={1651-1664} }

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.

## 47 Citations

### SUSY Quantum Mechanics for PT Symmetric Systems

- Physics
- 2018

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

- Physics
- 2004

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

- Physics
- 2004

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

- Physics
- 2005

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

- Physics
- 2006

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

- Physics, Mathematics
- 2005

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…

### ${\mathcal{PT}}$-SYMMETRIC SUPERSYMMETRY IN A SOLVABLE SHORT-RANGE MODEL

- Physics
- 2005

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

- Physics
- 2004

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

- Physics
- 2004

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

- Mathematics, Physics
- 2006

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…

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