QUANTUM MECHANICAL SOLUTION OF A DAMPED HARMONIC OSCILLATOR WITH TIME-DEPENDENT PARAMETERS

1985 ◽  
Vol 5 (3) ◽  
pp. 319-325
Author(s):  
Honghua Xu
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Damped Harmonic Oscillator ◽  
Quantum Mechanical Solution

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.

scholarly journals Integrals of the motion and green functions for time-dependent mass harmonic oscillators

2018 ◽  
Vol 64 (1) ◽  
pp. 30
Author(s):  
Surarit Pepore
Keyword(s):  
Harmonic Oscillator ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Green Functions ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Damped Harmonic Oscillator ◽  
System Trajectory ◽  
Dependent Mass ◽  
Motion Method

The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Greenfunction is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phasespace. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsatingmass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between theintegrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.

scholarly journals Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 4 (1) ◽  
pp. 47-55
Author(s):  
Timothy Brian Huber
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Mechanical System ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Quantum Mechanical System ◽  
Intertwining Operator

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

scholarly journals Constructing the time independent Hamiltonian from a time dependent one

Open Physics ◽  
2007 ◽  
Vol 5 (3) ◽  
Author(s):  
Michał Dobrski
Keyword(s):  
Dynamical System ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Hamiltonian Dynamical System ◽  
Equivalent Time ◽  
New Time

AbstractIn this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.

TIME-DEPENDENT BOGOLIUBOV TRANSFORMATIONS AND THE DAMPED HARMONIC OSCILLATOR

1993 ◽  
Vol 08 (21) ◽  
pp. 1999-2009
Author(s):  
P. SHANTA ◽  
S. CHATURVEDI ◽  
V. SRINIVASAN ◽  
F. MANCINI
Keyword(s):  
Harmonic Oscillator ◽  
Master Equation ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Bogoliubov Transformations ◽  
Non Equilibrium

We derive the master equation for a damped harmonic oscillator, for any α, using time-dependent Bogoliubov transformations of non-equilibrium thermofield dynamics. This investigation naturally leads us to a physically and mathematically meaningful parametrization of the Bogoliubov matrix.

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