Time Evolution of Quantum-Mechanical Harmonic Oscillator with Time-Dependent Frequency

2008 ◽  
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Dependent Frequency

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.

Algebraic time-ordering techniques and harmonic oscillator with time-dependent frequency

1986 ◽  
Vol 34 (4) ◽  
pp. 2646-2653 ◽  
Author(s):  
G. Dattoli ◽  
S. Solimeno ◽  
A. Torre
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Dependent Frequency

Time Evolution of the Time-Dependent Harmonic Oscillator

1998 ◽  
Vol 29 (3) ◽  
pp. 385-388 ◽  
Author(s):  
Xu Jingbo ◽  
Yu Youhong
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent

Time evolution of a time-dependent inverted harmonic oscillator in arbitrary dimensions

2012 ◽  
Vol 45 (11) ◽  
pp. 115301
Author(s):  
Guang-Jie Guo ◽  
Zhong-Zhou Ren ◽  
Guo-Xing Ju ◽  
Xiao-Yong Guo
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Time Dependent ◽  
Arbitrary Dimensions

SQUEEZING AND SOME OTHER CHARACTERISTICS OF TIME-DEPENDENT HARMONIC OSCILLATOR WITH VARIABLE MASS

1994 ◽  
Vol 08 (14n15) ◽  
pp. 917-927 ◽  
Author(s):  
A. JOSHI ◽  
S. V. LAWANDE
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Time Evolution ◽  
Evolution Operator ◽  
Variable Mass ◽  
Time Dependent ◽  
Integral Approach ◽  
Feynman Path ◽  
Time Evolution Operator ◽  
General Time

In this paper we investigate the time evolution of a general time-dependent harmonic oscillator (TDHO) with variable mass using Feynman path integral approach. We explicitly evaluate the squeezing in the quadrature components of a general quantum TDHO with variable mass. This calculation is further elaborated for three particular cases of variable mass whose propagator can be written in a closed form. We also obtain an exact form of the time-evolution operator, the wave function, and the time-dependent coherent state for the TDHO. Our results clearly indicate that the time-dependent coherent state is equivalent to the squeezed coherent state.

NEW NONCLASSICAL SOLUTION ON GENERALIZED PAUL TRAP TYPE: NONCLASSICAL STUDY

2000 ◽  
Vol 15 (16) ◽  
pp. 1071-1078
Author(s):  
BISWANATH RATH
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Annihilation Operator ◽  
Paul Trap ◽  
Simple Expression ◽  
Creation Operator ◽  
Time Dependent ◽  
Dependent Frequency ◽  
Generalized Time

New nonclassical solutions for the harmonic oscillator with generalized time-dependent frequency have been found. Simple expression on energy level, creation operator a†(t) and annihilation operator a(t) have been obtained. Using new solutions we want to show how to study squeezing.

Squeezing caused by a change of mass in a harmonic oscillator

1989 ◽  
Vol 67 (2-3) ◽  
pp. 152-154 ◽  
Author(s):  
Fan Hong-Yi ◽  
H. R. Zaidi
Keyword(s):  
Harmonic Oscillator ◽  
Time Evolution ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Mass Change ◽  
Transformation Time

It is shown that a mass change in a harmonic oscillator generates a squeezing transformation. Time-independent as well as time-dependent transformations are investigated. An expression for the interaction Hamiltonian responsible for squeezing and the equations of motion for the time evolution are derived.

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