Coherent states for Hamiltonians generated by supersymmetry

Abstract

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poeschl-Teller potentials.

LaTeX file, 26 pages, 3 eps figures

References in corpus (37)

• f-Oscillators and Nonlinear Coherent States
• Higher-Derivative Supersymmetry and the Witten Index
• Second Order Derivative Supersymmetry and Scattering Problem
• A family of complex potentials with real spectrum
• Universal Superpositions of Coherent States and Self-Similar Potentials
• Higher-order supersymmetric quantum mechanics
• N-fold Supersymmetry in Quantum Mechanics - General Formalism -
• New nonlinear coherent states and some of their nonclassical properties
• The finite difference algorithm for higher order supersymmetry
• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• Nonlinear Supersymmetry for Spectral Design in Quantum Mechanics
• The Construction of Some Important Classes of Generalized Coherent states: The Nonlinear Coherent States Method
• Shape-invariant potentials and an associated coherent state
• General Forms of a N-fold Supersymmetric Family
• New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
• SUSUSY quantum mechanics
• The confluent algorithm in second order supersymmetric quantum mechanics
• Group theoretical approach to the intertwined Hamiltonians
• Distorted Heisenberg Algebra and Coherent States for Isospectral Oscillator Hamiltonians
• Coherent States of Non-Linear Lie algebras: Application in Quantum Optics
• Symplectic tomography of nonlinear coherent states of a trapped ion
• Symplectic Tomography of Nonclassical States of Trapped Ion
• Wronskian formula for confluent second-order supersymmetric quantum mechanics
• SUSY Intertwining Relations of Third Order in Derivatives
• Coherent states for exactly solvable potentials
• Superconformal mechanics and nonlinear supersymmetry
• A New Family of N-fold Supersymmetry: Type B
• Fock-Bargman Representation of the Distorted Heisenberg Algebra
• Generalized Coherent States Associated with the $C_{\lambda }$-Extended Oscillator
• Generalized coherent states associated with the C_λ-extended oscillator
• Coherent states of P{ö}schl-Teller potential and their revival dynamics
• Application of nonlinear deformation algebra to a physical system with Pöschl-Teller potential
• Supersymmetric Hubbard Operators
• Coherent States for Isospectral Hamiltonians
• Nonlinear supersymmetry: from classical to quantum mechanics
• Ladder operators for isospectral oscillators
• Isospectral Hamiltonians and $W_{1+\infty }$ algebra

Cited by in corpus (37)

• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Position Dependent Mass Oscillators and Coherent States
• Superintegrability and higher order polynomial algebras I
• Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
• Supersymmetric partners of the trigonometric Poschl-Teller potentials
• Trends in supersymmetric quantum mechanics
• Generalized coherent states for time-dependent and nonlinear Hamiltonians via complex Riccati equations
• Quons, coherent states and intertwining operators
• On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
• Coherent state of a nonlinear oscillator and its revival dynamics
• Vector coherent states and intertwining operators
• SU(1,1) Coherent States For Position-Dependent Mass Singular Oscillators
• Completeness and Nonclassicality of Coherent States for Generalized Oscillator Algebras
• Coherent states approach to Penning trap
• Coherent and squeezed states: introductory review of basic notions, properties and generalizations
• On the position dependent effective mass Hamiltonian
• A pedestrian introduction to coherent and squeezed states
• Coherent states for the supersymmetric partners of the truncated oscillator
• Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum
• Painlevé IV Coherent States
• Pöschl-Teller Hamiltonian: Gazeau-Klauder type coherent states, related statistics and geometry
• Coherent states for quadratic Hamiltonians
• Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
• Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians
• An introductory review on resource theories of generalized nonclassical light
• On the ladder operators and nonclassicality of generalized coherent state associated with a particle in an infinite square well
• Ladder operators and squeezed coherent states of a 3-dimensional generalized isotonic nonlinear oscillator
• Susy for non-Hermitian Hamiltonians, with a view to coherent states
• Infinite square-well, trigonometric Pöschl-Teller and other potential wells with a moving barrier
• Degeneracy and coherent states of the two-dimensional Morse potential
• Supersymmetric Quantum Mechanics, multiphoton algebras and coherent states
• On the general family of third-order shape-invariant Hamiltonians related to generalized Hermite polynomials
• Quantum square well with logarithmic central spike
• Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• An approach to construct wave packets with complete classical-quantum correspondence in non-relativistic quantum mechanics
• New coherent states with Laguerre polynomials coefficients for the symmetric Poschl-Teller oscillator
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions