Application of nonlinear deformation algebra to a physical system with Pöschl-Teller potential

Abstract

We comment on a recent paper by Chen, Liu, and Ge (J. Phys. A: Math. Gen. 31 (1998) 6473), wherein a nonlinear deformation of su(1,1) involving two deforming functions is realized in the exactly solvable quantum-mechanical problem with P\" oschl-Teller potential, and is used to derive the well-known su(1,1) spectrum-generating algebra of this problem. We show that one of the defining relations of the nonlinear algebra, presented by the authors, is only valid in the limiting case of an infinite square well, and we determine the correct relation in the general case. We also use it to establish the correct link with su(1,1), as well as to provide an algebraic derivation of the eigenfunction normalization constant.

9 pages, LaTeX, no figures

Cited by in corpus (13)

• Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
• Coherent states for Hamiltonians generated by supersymmetry
• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems
• Coherent states of P{ö}schl-Teller potential and their revival dynamics
• Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework
• Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential
• Poeschl-Teller paradoxes
• Analytic Expression for Exact Ground State Energy Based on an Operator Method for a Class of Anharmonic Potentials
• A unified approach for exactly solvable potentials in quantum mechanics using shift operators
• On the ladder operators and nonclassicality of generalized coherent state associated with a particle in an infinite square well
• Quantum Dynamical Algebra SU(1,1) in One-Dimensional Exactly Solvable Potentials
• Solving the Jaynes-Cummings Model with Shift Operators Constructed by Means of the Matrix-Diagonalizing Technique