Trends in Supersymmetric Quantum Mechanics

  title={Trends in Supersymmetric Quantum Mechanics},
  author={David J Fern{\'a}ndez C},
  journal={Integrability, Supersymmetry and Coherent States},
  • David J Fernández C
  • Published 15 November 2018
  • Physics
  • Integrability, Supersymmetry and Coherent States
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… 

Confluent second-order supersymmetric quantum mechanics and spectral design

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

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

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

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

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

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

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 $W(x,A,B)=A\tanh 3px-B\coth px$

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

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



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

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

Supersymmetric quantum mechanics of one-dimensional systems

It is shown that every one-dimensional quantum mechanical Hamiltonian H1 can have a partner H2 such that H1 and H2 taken together may be viewed as the components of a supersymmetric Hamiltonian. The

Progress in supersymmetric quantum mechanics

The idea of preparing a special issue devoted to supersymmetric quantum mechanics (SUSY QM) emerged during the course of the International Conference on Progress in Supersymmetric Quantum Mechanics

Nonlinear supersymmetric quantum mechanics: concepts and realizations

The nonlinear supersymmetric (SUSY) approach to spectral problems in quantum mechanics (QM) is reviewed. Its building from the chains (ladders) of linear SUSY systems is outlined and different

SUSUSY Quantum Mechanics

The exactly solvable eigenproblems in Schrodinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to

Supersymmetric quantum mechanics and its applications

The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this

Inverse scattering with supersymmetric quantum mechanics

The application of supersymmetric quantum mechanics to the inverse scattering problem is reviewed. The main difference with standard treatments of the inverse problem lies in the simple and natural

Supersymmetric quantum mechanics and Painlevé equations

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial