The hidden symmetry for a quantum system with an infinitely deep square-well potential

2002 ◽  
Vol 70 (5) ◽  
pp. 520-521 ◽  
Author(s):  
Shi-Hai Dong ◽  
Zhong-Qi Ma
Keyword(s):  
Quantum System ◽  
Hidden Symmetry ◽  
Square Well

scholarly journals COHERENT AND GENERALIZED INTELLIGENT STATES FOR INFINITE SQUARE WELL POTENTIAL AND NONLINEAR OSCILLATORS

2002 ◽  
Vol 16 (26) ◽  
pp. 3915-3937 ◽  
Author(s):  
A. H. EL KINANI ◽  
M. DAOUD
Keyword(s):  
Quantum System ◽  
Coherent States ◽  
Nonlinear Oscillators ◽  
Analytical Representation ◽  
Square Well ◽  
Arbitrary Quantum

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

The Wigner Function for a Quantum System with an Infinitely Deep Square-Well Potential

2004 ◽  
Vol 70 (4) ◽  
pp. 207-211 ◽  
Author(s):  
Shi-Hai Dong ◽  
Guo-Hua Sun ◽  
Jiang Yu
Keyword(s):  
Quantum System ◽  
Wigner Function ◽  
Square Well

THE HIDDEN SYMMETRY FOR A QUANTUM SYSTEM WITH A PÖSCHL–TELLER-LIKE POTENTIAL

2003 ◽  
Vol 12 (06) ◽  
pp. 809-815 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
YU TANG
Keyword(s):  
Quantum System ◽  
Wave Functions ◽  
Matrix Elements ◽  
Eigenvalues And Eigenfunctions ◽  
Creation And Annihilation Operators ◽  
Commutation Relations ◽  
Hidden Symmetry ◽  
The Matrix ◽  
The Creation ◽  
Analytical Expressions

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 POSITION-DEPENDENT MASS SCHRÖDINGER EQUATION FOR A SINGULAR OSCILLATOR

2007 ◽  
Vol 22 (14) ◽  
pp. 1039-1045 ◽  
Author(s):  
SHI-HAI DONG ◽  
J. J. PEÑA ◽  
C. PACHECO-GARCÍA ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Schrödinger Equation ◽  
Quantum System ◽  
Effective Mass ◽  
Lie Algebra ◽  
Schrodinger Equation ◽  
Algebraic Approach ◽  
Hidden Symmetry ◽  
Dependent Mass ◽  
Complete Solutions ◽  
Position Dependent Mass

We construct a singular oscillator Hamiltonian with a position-dependent effective mass. We find that an su(1, 1) algebra is the hidden symmetry of this quantum system and the isospectral potentials V(x) depend on the different choices of the m(x). The complete solutions are also presented by using this Lie algebra.

REALIZATION OF DYNAMICAL GROUP FOR A SYMMETRIC WELL POTENTIAL tan2(πx/a) AND ITS CONTROLLABILITY

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5833-5843
Author(s):  
SHI-HAI DONG ◽  
M. LOZADA-CASSOU ◽  
MARCO A. ARJONA L
Keyword(s):  
Exact Solutions ◽  
Quantum System ◽  
Ground State ◽  
Bound States ◽  
Factorization Method ◽  
Creation Operator ◽  
Ladder Operators ◽  
Dynamical Group ◽  
Commutation Relations ◽  
Square Well

The exact solutions of quantum system with a symmetric well potential V(x) = D tan 2(πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator [Formula: see text] on the ground state.

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