The Hidden Symmetry for a Quantum System With a Pöschl–teller-Like Potential

Abstract

The eigenvalues and eigenfunctions of the Schrödinger equation with a Pöschl–Teller (PT)-like potential are presented. A realization of the creation and annihilation operators for the wave functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions, sin (ρ) and [Formula: see text] with ρ=πx/L.

Algebraic Approach to the Hulthen Potential

“…It is clear that systems displaying a dynamical symmetry can be treated by algebraic methods (Arima and Iachello, 1974;Perelomov, 1985;Wybourne, 1974;Cooper, 1993). To see the ladder operators of a quantum system with some important potentials such as Morse potential the Pöschel-Teller one, the pseudo harmonic one, the infinitely square-well one and other quantum systems refer to , , Dong (2002a,b), Dong and Ma (2002a,b), Dong and Dong (2002a,b), Dong (2003Dong ( , 2004, Dong et al (2003).…”

Exact Solutions of the Morse-like Potential, Step-Up and Step-Down Operators via Laplace Transform Approach

“…whereL + is the step-up operator with eigenvalue ℓ + andL − is the step-up operator with eigenvalue ℓ − and having the form [16][17][18][19][20][21][22][23] L…”

“…Finally we study the Lie algebra associated to the operatorsL ± to construct the commutator of them with the help of Eqs. (22) and (26):…”

Realization of the Spectrum Generating Algebra for the Generalized Kratzer Potentials

“…quantum systems have been established [5][6][7][8][9][10][11][12][13][14]. For comprehensive review (see Dong and references therein [4]).…”

“…In 2007, Rasinariu et al [15] gave a review of the progress made so far in solving exactly solvable problems in quantum mechanics, by connecting supersymmetry and spectrum generating algebras through the property of shape invariance. The solutions of exactly solvable models can be achieved by dynamical algebraic approaches [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][18][19][20][21]. In 1991, De Lange and Raab [16] presented operator methods with shift operators (that is, raising and lowering operators) for the Hamiltonian of exactly solvable models.…”