Exact propagator for a time−dependent harmonic oscillator with and without a singular perturbation

1975 ◽  
Vol 16 (2) ◽  
pp. 384 ◽  
Author(s):  
D. C. Khandekar
Keyword(s):  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Time Dependent

Exact Solution of a Time‐Dependent Quantal Harmonic Oscillator with a Singular Perturbation

1971 ◽  
Vol 12 (10) ◽  
pp. 2040-2043 ◽  
Author(s):  
P. Camiz ◽  
A. Gerardi ◽  
C. Marchioro ◽  
E. Presutti ◽  
E. Scacciatelli
Keyword(s):  
Exact Solution ◽  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Time Dependent

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.

QUANTUM STATES WITH CONTINUOUS SPECTRUM FOR THE TIME-DEPENDENT HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

2007 ◽  
Vol 21 (10) ◽  
pp. 585-593 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
JUN-YOUNG OH
Keyword(s):  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Continuous Spectrum ◽  
Unitary Operator ◽  
Energy Eigenvalue ◽  
Invariant Operator ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Discrete Energy

The quantum states with continuous spectrum for the time-dependent harmonic oscillator perturbed by a singularity are investigated. This system does not oscillate while the system that has discrete energy eigenvalue does. Exact wave functions satisfying the Schrödinger equation for the system are derived using invariant operator and unitary operator together.

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

scholarly journals Time-dependent propagator for an-harmonic oscillator with quartic term in potential

2021 ◽  
Vol 62 (2) ◽  
pp. 023501
Author(s):  
J. Boháčik ◽  
P. Prešnajder ◽  
P. Augustín
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Quartic Term
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