Shape-invariant potentials and an associated coherent state

Abstract

An algebraic treatment of shape-invariant potentials in supersymmetric quantum mechanics is discussed. By introducing an operator which reparametrizes wave functions, the shape-invariance condition can be related to a oscillator-like algebra. It makes possible to define a coherent state associated with the shape-invariant potentials. For a large class of such potentials, it is shown that the introduced coherent state has the property of resolution of unity.

11 pages + 1 figure (not included),Plain Tex YITP/K-1019, RCNP-055

References in corpus (1)

• Exactly Solvable Potentials and Quantum Algebras

Cited by in corpus (36)

• Supersymmetry and Quantum Mechanics
• Algebraic Approach to Shape Invariance
• Coherent states for Hamiltonians generated by supersymmetry
• Algebraic Nature of Shape-Invariant and Self-Similar Potentials
• Exact solution in the Heisenberg picture and annihilation-creation operators
• Discrete Quantum Mechanics
• An Algebraic Construction of Generalized Coherent States for Shape-Invariant Potentials
• Generalized Heisenberg algebra coherent states for Power-law potentials
• Shape invariance, raising and lowering operators in hypergeometric type equations
• Generalized $su(1,1)$ coherent states for pseudo harmonic oscillator and their nonclassical properties
• Barut-Girardello coherent states for nonlinear oscillator with position-dependent mass
• Coherent states of nonlinear oscillators with position-dependent mass: the temporal stability and fractional revivals
• Coherent state of a nonlinear oscillator and its revival dynamics
• Creation and annihilation operators and coherent states for the PT-symmetric oscillator
• Coherent States for Transparent Potentials
• Generalized coherent states for position-dependent effective mass systems
• A pedestrian introduction to coherent and squeezed states
• Shape Invariant Potentials in Supersymmetric Quantum Cosmology
• Generalized Ladder Operators for the Dirac-Coulomb Problem via SUSY QM
• Generalized Ladder Operators for Shape-invariant Potentials
• Generalized $su(2)$ coherent states for the Landau levels and their nonclassical properties
• Potential algebra approach to position dependent mass Schroedinger equation
• Generalized Coherent States for the Spherical Harmonics $Y_m^m(\theta ,\varphi )$
• A unified approach for exactly solvable potentials in quantum mechanics using shift operators
• Coherent state of the effective mass harmonic oscillator
• Algebraic approach for shape invariant potentials in Klein-Gordon equation
• Self-Similar Potentials and q-Coherent States
• General Displaced SU (1,1) number states-revisited
• Exactness of Semiclassical Quantization Rule for Broken Supersymmetry
• Ladder operators for subtle hidden shape invariant potentials
• Coherent State for a Relativistic Spinless Particle
• Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials
• Generalized Langer Correction and the Exactness of WKB for all Conventional Potentials
• An approach to construct wave packets with complete classical-quantum correspondence in non-relativistic quantum mechanics
• Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties
• Ladder operators and coherent states for the Rosen-Morse system and its rational extensions