## 2,105 Citations

### Supersymmetry in quantum mechanics

- Physics
- 1997

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

- Physics
- 2019

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

- Mathematics, Physics
- 2012

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

- Physics
- 2012

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

- Physics
- 2022

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

- PhysicsPhysics 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

- PhysicsIntegrability, Supersymmetry and Coherent States
- 2019

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

- Physics, MathematicsJournal of High Energy Physics
- 2021

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

- Physics
- 2011

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)…

### Exactly solvable new classes of potentials with finite discrete energies

- PhysicsResults in Physics
- 2020

## References

SHOWING 1-10 OF 229 REFERENCES

### Supersymmetry in Quantum Mechanics

- Physics
- 1990

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.

- 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.

### Supersymmetry in Quantum Mechanics

- Physics
- 1986

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…

### NEW FINDINGS IN QUANTUM MECHANICS (PARTIAL ALGEBRAIZATION OF THE SPECTRAL PROBLEM)

- Physics, Mathematics
- 1989

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

- 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…

### Recent Developments in Gauge Theories

- Physics
- 1980

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

- Physics
- 1991

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

- Physics
- 1982

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…