EXACT SOLUTIONS, LADDER OPERATORS AND BARUT–GIRARDELLO COHERENT STATES FOR A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL

2005 ◽  
Vol 19 (28) ◽  
pp. 4219-4227 ◽  
Author(s):  
SHI-HAI DONG ◽  
M. LOZADA-CASSOU
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Coherent States ◽  
Factorization Method ◽  
Ladder Operators ◽  
Dynamical Group ◽  
One Dimensional ◽  
Hidden Symmetry ◽  
The One ◽  
Analytical Expressions

We present exact solutions of the one-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential. The ladder operators are constructed by the factorization method. We find that these operators satisfy the commutation relations of the generators of the dynamical group SU(1, 1). Based on those ladder operators, we obtain the analytical expressions of matrix elements for some related functions ρ and [Formula: see text] with ρ=x2. Finally, we make some comments on the Barut–Girardello coherent states and the hidden symmetry between E(x) and E(ix) by substituting x→ix.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

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.

scholarly journals On The Information-Theoretical Entropy for Some Quantum Oscillators

2013 ◽  
Vol 57 (1) ◽  
pp. 67-79
Author(s):  
Dušan Popov ◽  
Nicolina Pop ◽  
Simona Șimon
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Wehrl Entropy ◽  
One Dimensional ◽  
The One ◽  
Classical Entropy ◽  
Thermal States

Abstract The information-theoretical entropy, also called the “classical” entropy, was introduced by Wehrl in terms of the Glauber coherent states (CSs) | z > , i.e. the CSs corresponding to the one-dimensional harmonic oscillator (HO-1D). In the present paper, we have focused our attention on the examination of the information-theoretical entropy, i.e. the Wehrl entropy, for both the pure and the mixed (thermal) states of some quantum oscillators.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media

2019 ◽  
Vol 34 (6) ◽  
pp. 339-351 ◽  
Author(s):  
Petr S. Kondratenko ◽  
Leonid V. Matveev ◽  
Alexander D. Vasiliev
Keyword(s):  
Numerical Modelling ◽  
Contaminant Transport ◽  
Integral Kernel ◽  
Time Intervals ◽  
One Dimensional ◽  
Time Representation ◽  
Impurity Transport ◽  
The One ◽  
Analytical Expressions ◽  
Good Agreement

Abstract A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting time intervals in the one-dimensional case are derived. An interpolation form is proposed for the integral kernel of the transport equation. On a basis of this expression, an algorithm is developed for numerical modelling the contaminant transport in statistically homogeneous sharply contrasting media. Trial numerical 1D calculations are performed based on this algorithm. Good agreement was found between the numerical simulation results and the asymptotic analytical expressions.

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

Quantum mechanics on (anti)-de Sitter background II: Ramsauer–Townsend effect and WKB method

2018 ◽  
Vol 33 (26) ◽  
pp. 1850150 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Wkb Method ◽  
De Sitter ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Sitter Background ◽  
The One

Based on the one-dimensional quantum mechanics on (anti)-de Sitter background [W. S. Chung and H. Hassanabadi, Mod. Phys. Lett. A 32, 26 (2107)], we discuss the Ramsauer–Townsend effect. We also formulate the WKB method for the quantum mechanics on (anti)-de Sitter background to discuss the energy level of the quantum harmonic oscillator and quantum bouncer.

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