QUANTUM TREATMENT OF TIME DEPENDENT COUPLED OSCILLATORS

2002 ◽  
Vol 16 (19) ◽  
pp. 2837-2855 ◽  
Author(s):  
M. SEBAWE ABDALLA
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Invariants ◽  
Quantum Treatment ◽  
Schrödinger Picture

In this paper we consider the most quadratic time dependent Hamiltonian. An exact solution of the wave function in both the Schrödinger picture and coherent states representation is given. Linear and quadratic invariants are discussed. The eigenvalues and the corresponding eigenfunctions are obtained. The expectation values for the energy are also given.

QUANTUM TREATMENT OF THREE MUTUALLY ANISOTROPIC COUPLED OSCILLATORS

2006 ◽  
Vol 20 (24) ◽  
pp. 3487-3505 ◽  
Author(s):  
M. M. NASSAR ◽  
M. SEBAWE ABDALLA
Keyword(s):  
Wave Function ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Quantum Mechanical ◽  
Long Period ◽  
Quantum Mechanical Treatment ◽  
Coupling Parameters ◽  
Quantum Treatment ◽  
Schrödinger Picture ◽  
Full Quantum

A full quantum mechanical treatment of the problem of three electromagnetic fields is considered. The system consists of three different coupling parameters where the rotating and counter-rotating terms are presented. An exact solution of the wave function in the Schrödinger picture is obtained, and the connection to the coherent states wave function is given. The symmetrical ordered quasi-probability distribution function (W-Wigner function) is calculated via the wave function in the coherent states representation. The Green's function is obtained and employed to find the Bloch density matrix. The expectation value of the energy is also given. In the framework of the vacuum and even coherent states, we have discussed the phenomenon of squeezing. It has been shown that the collapse and revival phenomenon exists at ω1=ω2 and is apparent for a long period of time.

scholarly journals QUANTUM KALB–RAMOND FIELD IN D-DIMENSIONAL DE SITTER SPACE–TIMES

2013 ◽  
Vol 28 (05n06) ◽  
pp. 1350011
Author(s):  
G. ALENCAR ◽  
I. GUEDES ◽  
R. R. LANDIM ◽  
R. N. COSTA FILHO
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Quantum Theory ◽  
De Sitter Space ◽  
Equation Of Motion ◽  
Time Dependent ◽  
De Sitter ◽  
Sitter Background ◽  
Dynamic Invariant ◽  
Math Phys

In this work, we investigate the quantum theory of the Kalb–Ramond fields propagating in D-dimensional de Sitter space–times using the dynamic invariant method developed by Lewis and Riesenfeld [J. Math. Phys.10, 1458 (1969)] to obtain the solution of the time-dependent Schrödinger equation. The wave function is written in terms of a c-number quantity satisfying the Milne–Pinney equation, whose solution can be expressed in terms of two independent solutions of the respective equation of motion. We obtain the exact solution for the quantum Kalb–Ramond field in the de Sitter background and discuss its relation with the Cremmer–Scherk–Kalb–Ramond model.

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.

A QUANTUM-MECHANICAL MODEL FOR AN LC CIRCUIT WITH ELASTIC CAPACITOR

2013 ◽  
Vol 27 (18) ◽  
pp. 1350138 ◽  
Author(s):  
M. CALCINA NOGALES
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Mechanical Model ◽  
Degrees Of Freedom ◽  
Complete System ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical Model ◽  
Lc Circuit ◽  
Dependent Probability

In this paper, we consider a quantum-mechanical LC circuit connected to a periodic source and with elastic capacitor. In the limit of negligible inductor energy, we present explicitly an exact solution for the wave function and spectrum of the spring-capacitor-source system. Considering the inductor energy as a perturbative term, the time-dependent probability amplitudes for the complete system are derived. We show that the mechanical degrees of freedom lead a suppression of the capacitor's charging/discharging process. Finally, we show the existence of a class of memristive component due to charge discreteness.

SU(1,1) LIE ALGEBRA APPLIED TO THE TIME-DEPENDENT QUADRATIC HAMILTONIAN SYSTEM PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (26) ◽  
pp. 3429-3441 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
SEONG SOO CHOI
Keyword(s):  
Hamiltonian System ◽  
Probability Density ◽  
Lie Algebra ◽  
Time Evolution ◽  
Coherent States ◽  
Classical Trajectory ◽  
Quantum States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Hamiltonian

We realized SU (1,1) Lie algebra in terms of the appropriate SU (1,1) generators for the time-dependent quadratic Hamiltonian system perturbed by a singularity. Exact quantum states of the system are investigated using SU (1,1) Lie algebra. Various expectation values in two kinds of the generalized SU (1,1) coherent states, that is, BG coherent states and Perelomov coherent states are derived. We applied our study to the CKOPS (Caldirola–Kanai oscillator perturbed by a singularity). Due to the damping constant γ, the probability density of the SU (1,1) coherent states for the CKOPS converged to the center with time. The time evolution of the probability density in SU (1,1) coherent states for the CKOPS are very similar to the classical trajectory.

WAVE FUNCTIONS OF TIME-DEPENDENT TWO COUPLED OSCILLATORS BY LEWIS–RIESENFELD METHOD

2006 ◽  
Vol 20 (09) ◽  
pp. 1087-1096 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHONG-HUA JIANG
Keyword(s):  
Schrödinger Equation ◽  
Operator Theory ◽  
Coupled Oscillators ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
General Solutions ◽  
Eigenvectors And Eigenvalues

For the two time-dependent coupled oscillators model we derive its time-dependent invariant in the context of Lewis–Riesenfeld invariant operator theory. It is based on the general solutions to the Schrödinger equation which is obtained and turns out to be the superposition of the generalized atomic coherent states in the Schwinger bosonic realization. The energy eigenvectors and eigenvalues of the corresponding time-independent Hamiltonian are also obtained as a by-product.

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