Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations

Abstract

Nonlinear SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. Possible multidimensional extensions of Nonlinear SUSY are described. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. Emergence of hidden symmetries and spectrum generating algebras is elucidated in the context of Nonlinear SUSY in one- and two-dimensional QM.

75 pages, Minor corrections, Version published in Journal of Physics A

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• Trends in supersymmetric quantum mechanics
• Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability
• Super Kähler oscillator from SU(2|1) superspace
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• SU(1,1) and SU(2) Approaches to the Radial Oscillator: Generalized Coherent States and Squeezing of Variances
• New solutions for graphene with scalar potentials by means of generalized intertwining
• Ladder operators for solvable potentials connected with exceptional orthogonal polynomials
• Coherent states for the supersymmetric partners of the truncated oscillator
• Self-similar potentials in quantum mechanics and coherent states
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Gravity effects on thick brane formation from scalar field dynamics
• Nonlinear supersymmetry as a hidden symmetry
• Supersymmetrization of the Franke-Gorini-Kossakowski-Lindblad-Sudarshan equation
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• New Implicitly Solvable Potential Produced by Second Order Shape Invariance
• Higher Order Supersymmetric Truncated Oscillators
• CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework
• A New Boson realization of Fusion Polynomial Algebras in Non-Hermitian Quantum Mechanics : $\gamma$-deformed $su(2)$ generators, Partial $\mathcal{P}\mathcal{T}$-symmetry and Higgs algebra
• Modular Operators and Entanglement in Supersymmetric Quantum Mechanics
• On the nonlocal Darboux transformation for the stationary axially symmetric Schrödinger and Helmholtz equations
• An affine Weyl group characterization of polynomial Heisenberg algebras
• A Note on Shape Invariant Potentials for Discretized Hamiltonians
• Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states
• Perturbation-based Non-perturbative Method
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation
• Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model
• Weak supersymmetry and superconformal indices
• Refractive index profiles for a $\mathcal{P}\mathcal{T}$-symmetric optical structure
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
• Dynamical symmetries of supersymmetric oscillators
• Applied Supersymmetry