Supersymmetric Quantum Mechanics

Abstract

Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric Poschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.

36 pages, 8 figures, lectures delivered at the Advanced Summer School 2009, Cinvestav (Mexico City), July 2009

References in corpus (1)

• The Quantum Mechanics SUSY Algebra: An Introductory Review

Cited by in corpus (43)

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• Wronskian differential formula for confluent supersymmetric quantum mechanics
• On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
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• Non-hermitian Hamiltonians and Painlevé IV equation with real parameters
• Supersymmetric Quantum Mechanics and Painlevé IV Equation
• Dirac Hamiltonian in a supersymmetric framework
• Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
• The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
• Bilayer graphene in magnetic fields generated by supersymmetry
• Supersymmetric partners of the harmonic oscillator with an infinite potential barrier
• Underlying SUSY in a generalized Jaynes-Cummings model
• The hyperbolic step potential: Antibound states, SUSY partners and Wigner time delays
• Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials
• Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design
• Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Solution hierarchies for the Painleve IV equation
• Extended WKB method, resonances and supersymmetric radial barriers
• So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation
• Supersymmetrization of the Franke-Gorini-Kossakowski-Lindblad-Sudarshan equation
• Coupled Supersymmetry and Ladder Structures Beyond the Harmonic Oscillator
• Extended supersymmetry with central charges in Dirac action with curved extra dimensions
• Twist Deformations of the Supersymmetric Quantum Mechanics
• Infinite square-well, trigonometric Pöschl-Teller and other potential wells with a moving barrier
• Supersymmetry Transformations for Delta Potentials
• Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian
• Extended supersymmetry with central charges in higher dimensional Dirac action
• Harmonic Oscillator SUSY Partners and Evolution Loops
• Darboux transformations and second order difference equations
• Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states
• 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 Potentials Analogs of Classical Electrostatic Fields
• Some Properties of the Shape Invariant Two-Dimensional Scarf II Model
• Dynamical symmetries of supersymmetric oscillators
• Exact electronic bands for a periodic Poschl-Teller potential
• Symmetries and Supersymmetries of Generalized Schrödinger equations
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
• Dirac-like Hamiltonians associated to Schrödinger factorizations
• Extended supersymmetry in Dirac action with extra dimensions