A brief introduction to the supersymmetric quantum mechanics (susy QM)

A. Frank, P. Van Isacker, Jan Jolie

F. Bagarello

Abstract We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.

S. Rajasekar, R. Velusamy

In the earlier chapters we presented basic features of certain advanced topics including supersymmetric quantum mechanics, coherent and squeezed states, quantum computers and quantum cryptography. There are several other topics which also received considerable interest and have a wide range of applications. In the present chapter we consider some of them. Particularly, we give a very brief introduction to the following fascinating topics: 1. Quantum gravity 2. Quantum Zeno effect 3. Quantum teleportation 4. Quantum games 5. Quantum cloning 6. Quantum diffusion 7. Quantum chaos.

A. Frank, Jan Jolie, Pieter Van Isacker

Fred Cooper, Avinash Khare, U. Sukhatme

BIJAN BAGCHI, A. BANERJEE, EMANUELA CALICETI +4 more

A brief overview is given of recent developments and fresh ideas at the intersection of [Formula: see text]- and/or [Formula: see text]-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of [Formula: see text]-symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator [Formula: see text] is represented in a differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator [Formula: see text], encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of [Formula: see text]-symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be [Formula: see text]-asymmetric.