Supersymmetry and quantum mechanics

  title={Supersymmetry and quantum mechanics},
  author={Fred Cooper and Avinash Khare and Uday P. Sukhatme},
  journal={Physics Reports},

Supersymmetry in quantum mechanics

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

Supersymmetric Quantum Mechanics and Path Integrals

Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. In this

Exceptional orthogonal polynomials and new exactly solvable potentials in quantum mechanics

In recent years, one of the most interesting developments in quantum mechanics has been the construction of new exactly solvable potentials connected with the appearance of families of exceptional

Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two

Shape Invariant Potentials in Supersymmetric Quantum Cosmology

In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of N=2 supersymmetric quantum mechanics. To motivate its application

How quantum mechanics probes superspace

  • S. Nicolis
  • Physics
    Physics of Particles and Nuclei Letters
  • 2017
We study quantum mechanics in one space dimension in the stochastic formalism. We show that the partition function of the theory is, in fact, equivalent to that of a model, whose action is explicitly

Trends in Supersymmetric Quantum Mechanics

Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the

Solitons in lattice field theories via tight-binding supersymmetry

Abstract Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of

Supersymmetric many-particle quantum systems with inverse-square interactions

The development in the study of supersymmetric many-particle quantum systems with inverse-square interactions is reviewed. The main emphasis is on quantum systems with dynamical OSp(2|2)



Supersymmetry in Quantum Mechanics

A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with

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

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.

Supersymmetry in Quantum Mechanics

We give some illustrations and interpretations of supersymmetry in quantum mechanics in simple models. We show that the value of 2 for the g factor of the electron expresses the presence of


We discuss a new class of spectral problems discovered recently which occupies an intermediate position between the exactly-solvable problems (like the famous harmonic oscillator) and all others. The

New shape invariant potentials in supersymmetric quantum mechanics

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

Recent Developments in Gauge Theories

Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified

Supersymmetry-inspired WKB approximation in quantum mechanics

The supersymmetry‐inspired WKB approximation (SWKB) in quantum mechanics is discussed in detail. The SWKB method can be easily applied to any potential whose ground‐state wave function is known. It

Large N limits as classical mechanics

This paper discusses the sense in which the large $N$ limits of various quantum theories are equivalent to classical limits. A general method for finding classical limits in arbitrary quantum