# Supersymmetry in quantum mechanics

@article{Khare1997SupersymmetryIQ, title={Supersymmetry in quantum mechanics}, author={Avinash Khare}, journal={Pramana}, year={1997}, volume={49}, pages={41-64} }

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications. I show that the well-known exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric…

## 95 Citations

A class of exactly solvable models to illustrate supersymmetry and test approximation methods in quantum mechanics

- Physics
- 2010

We obtain analytical expressions for the eigenvalues and eigenstates of a family of exponential-type potential wells. The supersymmetry formalism applied to quantum mechanics is summarized and…

The Quantum Mechanics Problem of the Schroedinger Equation with the Trigonometric Rosen-Morse Potential

- Physics
- 2006

We present the quantum mechanics problem of the one-dimensional Schroedinger equation with the trigonometric Rosen-Morse potential. This potential is of possible interest to quark physics in so far…

A new simple class of superpotentials in SUSY quantum mechanics

- Physics, Mathematics
- 2012

In this work, we introduce the class of quantum mechanics superpotentials W(x) = ge(x)x2n and study in detail the cases n = 0 and 1. The n = 0 superpotential is shown to lead to the known problem of…

Multi-Well Potentials in Quantum Mechanics and Stochastic Processes ?

- Physics
- 2010

Using the formalism of extended N = 4 supersymmetric quantum mechanics we consider the procedure of the construction of multi-well potentials. We demonstrate the form-invariance of Hamiltonians…

A novel connection between scalar field theories and quantum mechanics

- Physics
- 2018

This work deals with scalar field theories and supersymmetric quantum mechanics. The investigation is inspired by a recent result, which shows how to use the reconstruction mechanism to describe two…

A novel SUSY energy bound-states treatment of the Klein-Gordon equation with PT-symmetric and q-deformed parameter Hulthén potential

- Physics
- 2018

In this study, we focus on investigating the exact relativistic bound-state spectra for supersymmetric, PT -supersymmetric and non -Hermitian versions of the q -deformed parameter Hulthen potential.…

Algebraic Properties of the Shape Invariance Condition

- Physics
- 2014

Supersymmetry (SUSY) is the symmetry relating bosonic and fermionic degrees of freedom. Historically, supersymmetric quantum mechanics (SUSY QM) was proposed as a limiting theory to gain a better…

New supersymmetry-generated complex potentials with real spectra

- Physics
- 2015

A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation…

## References

SHOWING 1-10 OF 26 REFERENCES

New shape invariant potentials in supersymmetric quantum mechanics

- Physics
- 1993

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, the authors obtain a large…

Bound states in the continuum from supersymmetric quantum mechanics.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1993

This work compute and graph potentials which have bound states in the continuum starting from a null potential representing a free particle and from both the attractive and the repulsive Coulomb potentials.

New exactly solvable Hamiltonians: Shape invariance and self-similarity.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1993

A class of exactly solvable Hamiltonians is further enlarged by examining two new directions: changes of parameters which are different from the previously studied cases of translation and scaling and extending the usual concept of shape invariance in one step to a multistep situation.

Semiclassical approach to quantum-mechanical problems with broken supersymmetry.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1993

The semiclassical WKB approximation method is reexamined in the context of nonrelativistic quantum-mechanical bound-state problems with broken supersymmetry (SUSY) and it is shown that to leading order in [h bar], the BSWKB condition yields exact energy eigenvalues for shape-invariant potentials with broken SUSY which are known to be analytically solvable.

Exactly solvable noncentral potentials in two and three dimensions

- Physics, Mathematics
- 1994

We show that the list of analytically solvable potentials in nonrelativistic quantum mechanics can be considerably enlarged. In particular, we show that those noncentral potentials for which the…