COHERENT STATES OF NONCONSERVATIVE HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

2003 ◽  
Vol 17 (12) ◽  
pp. 2429-2437 ◽  
Author(s):  
JEONG RYEOL CHOI
Keyword(s):  
Singular Perturbation ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
Expectation Values ◽  
Raising Operators ◽  
The Difference

We investigated the coherent states of nonconservative harmonic oscillator with a singular perturbation. The invariant operator represented in terms of lowering and raising operators. We confirmed that if the difference between two eigenvalues, α and β, of coherent states is much larger than unity, the states |α> and |β> are approximately orthogonal to each another. We calculated the expectation values of various quantities such as invariant operator, Hamiltonian and mechanical energy in coherent state. The mechanical energy of the system described by the Kanai–Caldirola Hamiltonian decreased exponentially depending on γ as time goes by in coherent state.

OPERATOR METHOD FOR A NONCONSERVATIVE HARMONIC OSCILLATOR WITH AND WITHOUT SINGULAR PERTURBATION

2002 ◽  
Vol 16 (31) ◽  
pp. 4733-4742 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
BO HA KWEON
Keyword(s):  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Operator Method ◽  
Invariant Operator ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Ladder Operators ◽  
Raising Operators ◽  
Quantum Mechanical Solution

We used dynamical invariant operator method to find the quantum mechanical solution of a harmonic plus inverse harmonic oscillator with time-dependent coefficients. The eigenvalue of invariant operator is obtained and is constant with time. We constructed lowering and raising operators from the invariant operator. The solution of Schrödinger equation is obtained using operator method. We have also used ladder operators to obtain various expectation values of the time-dependent system. The results in this manuscript are not only more general than the existing results in the literatures but also well match with others.

Angular momentum coherent states

1971 ◽  
Vol 321 (1546) ◽  
pp. 321-340 ◽  
Keyword(s):  
Angular Momentum ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Classical Limit ◽  
Coherent States ◽  
Uncertainty Relations ◽  
Mean Square ◽  
Expectation Values ◽  
Angular Momenta ◽  
Two Component

The work of Carruthers & Nieto on the harmonic oscillator coherent states is combined with Schwinger’s construction of angular momentum to produce the angular momentum coherent states. It is shown that these states become the vector representatives of angular momentum in the classical limit, and so are particularly useful for discussing the transition from quantum to classical angular momentum. The uncertainty relations for angle and angular momentum are described and are compatible with the classical limit. Under rotations the coherent states transform in a manner that in the classical limit is equivalent to the transformation of vectors, and in the same limit the root mean square variation of the expectation values of the components of angular momentum become negligible in comparison with the expectation values themselves. The coupling of two angular momenta in the classical limit is investigated: it is shown that although the product of two coherent states is not itself a coherent state, it does represent a packet similar to a true coherent state, and centred on the direction of the classical resultant of the two component vectors. The properties and implications of hyperbolic angular momentum space are discussed.

INTERACTION OF MESOSCOPIC JOSEPHSON JUNCTION WITH A SUCCESSIVE SQUEEZED COHERENT FIELD

2000 ◽  
Vol 14 (16) ◽  
pp. 609-618
Author(s):  
V. A. POPESCU
Keyword(s):  
Coherent State ◽  
Josephson Junction ◽  
Coherent States ◽  
Quantum Noise ◽  
Shapiro Steps ◽  
Superconducting Ring ◽  
Coherent Field ◽  
Current Voltage ◽  
Quantum Current ◽  
The Difference

Signal-to-quantum noise ratio for quantum current in mesoscopic Josephson junction of a circular superconducting ring can be improved if the electromagnetic field is in a successive squeezed coherent state. The mesoscopic Josephson junctions can feel the difference between the successive squeezed coherent states and other types of squeezed coherent states because their current–voltage Shapiro steps are different. We compare our method with another procedure for superposition of two squeezed coherent states (a squeezed even coherent state) and consider the effect of different large inductances on the supercurrent.

scholarly journals COHERENT STATE OF THE EFFECTIVE MASS HARMONIC OSCILLATOR

2009 ◽  
Vol 24 (17) ◽  
pp. 1343-1353 ◽  
Author(s):  
ATREYEE BISWAS ◽  
BARNANA ROY
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Closed Form ◽  
Effective Mass ◽  
Coherent States ◽  
Mass Function ◽  
Wigner Functions

We construct coherent state of the effective mass harmonic oscillator and examine some of its properties. In particular closed form expressions of coherent states for different choices of the mass function are obtained and it is shown that such states are not in general x - p uncertainty states. We also compute the associated Wigner functions.

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.

scholarly journals COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I: MATHEMATICAL CONSTRUCTION

2013 ◽  
Vol 10 (10) ◽  
pp. 1350056 ◽  
Author(s):  
R. ROKNIZADEH ◽  
H. HEYDARI
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
One Dimensional ◽  
The Difference ◽  
Mathematical Construction

Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one-dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials [Formula: see text], bridging the difference between them is possible, we give here also the exact solution of Schrödinger equation of 1D NLHO in terms of Jacobi polynomials.

Adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator

2021 ◽  
pp. 2150201
Author(s):  
I. A. Pedrosa
Keyword(s):  
Harmonic Oscillator ◽  
Geometric Phase ◽  
Coherent States ◽  
Time Dependent ◽  
Expectation Values ◽  
Damped Harmonic Oscillator ◽  
Quantum Properties ◽  
Uncertainty Product ◽  
Dynamical Invariants ◽  
Damped Oscillator

In this work we present a simple and elegant approach to study the adiabatic and nonadiabatic evolution of a generalized damped harmonic oscillator which is described by the generalized Caldirola–Kanai Hamiltonian, in both classical and quantum contexts. Based on time-dependent dynamical invariants, we find that the geometric phase acquired when the damped oscillator evolves adiabatically in time provides a direct connection between the classical Hannay’s angle and the quantum Berry’s phase. In addition, we solve the time-dependent Schrödinger equation for this system and calculate various quantum properties of the damped generalized harmonic one, such as coherent states, expectation values of the position and momentum operators, their quantum fluctuations and the associated uncertainty product.

QUANTUM AND THERMAL STATE FOR EXPONENTIALLY DAMPED HARMONIC OSCILLATOR WITH AND WITHOUT INVERSE QUADRATIC POTENTIAL

2002 ◽  
Vol 16 (09) ◽  
pp. 1341-1351 ◽  
Author(s):  
J. R. CHOI
Keyword(s):  
Harmonic Oscillator ◽  
Density Operator ◽  
Thermal State ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
Diagonal Element ◽  
Quadratic Potential ◽  
Damped Harmonic Oscillator ◽  
Energy Expectation ◽  
Quantum Mechanical Energy

By taking advantage of dynamical invariant operator, we derived Schrödinger solution for exponentially damped harmonic oscillator with and without inverse quadratic potential. We investigated quantum mechanical energy expectation value, uncertainty relation, partition function and density operator of the system. The various expectation values in thermal state are calculated using the diagonal element of density operator.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

COHERENT STATE OF α-DEFORMED WEYL–HEISENBERG ALGEBRA

2013 ◽  
Vol 10 (05) ◽  
pp. 1350014 ◽  
Author(s):  
SH. DEHDASHTI ◽  
A. MAHDIFAR ◽  
R. ROKNIZADEH
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Heisenberg Algebra ◽  
Statistical Properties ◽  
Potential Well ◽  
Mandel Parameter ◽  
Boson Realization ◽  
Deformed Algebra

At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.

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