# Trends in Supersymmetric Quantum Mechanics

@article{FernndezC2018TrendsIS, title={Trends in Supersymmetric Quantum Mechanics}, author={David J Fern{\'a}ndez C}, journal={Integrability, Supersymmetry and Coherent States}, year={2018} }

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 spectral design. The key is to pair two Hamiltonians through a finite order differential operator. Some related subjects can be simply analyzed, as the algebras ruling both Hamiltonians and the associated coherent states. The technique has been applied also to periodic potentials, where the spectra…

## 23 Citations

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

- PhysicsResults in Physics
- 2020

### Confluent second-order supersymmetric quantum mechanics and spectral design

- PhysicsPhysica Scripta
- 2020

The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the…

### New solutions for graphene with scalar potentials by means of generalized intertwining

- PhysicsThe European Physical Journal Plus
- 2019

Abstract.The intertwining relations between superpartner Hamiltonians are the main ingredients of well-known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form…

### New solutions for graphene with scalar potentials by means of generalized intertwining

- PhysicsThe European Physical Journal Plus
- 2019

The intertwining relations between superpartner Hamiltonians are the main ingredients of well-known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form of…

### Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

The behavior of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, wherein two one-dimensional…

### Exactly Solvable Sextic Potential Having Symmetric Triple-Well Structure

- Physics
- 2020

In this paper, we introduce a family of sextic potentials that are exactly solvable, and for the first time, a family of triple-well potentials with their whole energy spectrum and wavefunctions…

### Supersymmetrization of the Lindblad-Franke-GKS equation

- Physics
- 2019

We investigate departures from hamiltonian dynamics of a SUSY quantum system due to its interaction with environment that generates decoherence. The Lindblad-Franke-GKS equation is taken to approach…

### Bilayer graphene in magnetic fields generated by supersymmetry

- Physics
- 2021

The effective Hamiltonian for electrons in bilayer graphene with applied magnetic fields is solved through second-order supersymmetric quantum mechanics. This method transforms the corresponding…

### Solvable Schrodinger Equations of Shape Invariant Potentials with Superpotential $W(x,A,B)=A\tanh 3px-B\coth px$

- Mathematics, Physics
- 2021

En (−) = (A − B) − (A − B − 4np), and the corresponding eigenfunctions determined exactly and in closed form. Schrödinger equations, and Sturm-Liouville equations in general, are challenging to solve…

### Extended supersymmetry with central charges in higher dimensional Dirac action

- PhysicsPhysical Review D
- 2019

A new realization of extended quantum-mechanical supersymmetry (QM SUSY) with central extension is investigated. We first show that two different sets of $d+2$ ($d+1$) supercharges for…

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