Harmonic Oscillators and Coherent States

2020 ◽  
pp. 105-127
Author(s):  
Rainer Dick
Keyword(s):  
Coherent States ◽  
Harmonic Oscillators

Coherent states for Smorodinsky-Winternitz potentials

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Nuri Ünal
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Wave Packets ◽  
Harmonic Oscillators ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Cartesian Coordinates ◽  
Physical Time ◽  
First Case

AbstractIn this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.

GENERALIZED DEFORMED HARMONIC OSCILLATORS IN THE FRAMEWORK OF UNIFIED (q; α, β, γ; ν)-DEFORMATION

2010 ◽  
Vol 25 (15) ◽  
pp. 1239-1249 ◽  
Author(s):  
I. M. BURBAN
Keyword(s):  
Coherent States ◽  
Anharmonic Oscillator ◽  
Harmonic Oscillators ◽  
Kerr Medium ◽  
Oscillator Algebra ◽  
Special Values ◽  
Deformation Parameters ◽  
Deformed Oscillator

The aim of this paper is the study of the generalized deformed quantum oscillators in the framework (q; α, β, γ; ν)-deformed of oscillator algebra. By selecting the special values of deformation parameters, we have separated a generalized deformed oscillator connected with generalized discrete Hermite II polynomials. By these means we have constructed Barut–Girardello type coherent states of this oscillator. We have found the conditions on the (q; α, β, γ; ν)-deformation parameters at which the free (q; α, β, γ; ν)-deformed oscillator approximate the usual anharmonic oscillator in the homogeneous Kerr medium.

Coupled harmonic oscillators, generalized harmonic-oscillator eigenstates and coherent states

1996 ◽  
Vol 111 (7) ◽  
pp. 811-823 ◽  
Author(s):  
G. Dattoli ◽  
A. Torre ◽  
S. Lorenzutta ◽  
G. Maino
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Generalized Harmonic Oscillator

Parametric-time coherent states for Morse potential

2002 ◽  
Vol 80 (8) ◽  
pp. 875-881 ◽  
Author(s):  
N Unal
Keyword(s):  
Coherent States ◽  
Morse Potential ◽  
Potential Problem ◽  
Path Integrals ◽  
Harmonic Oscillators

We transform the Lagrangian of the Morse-potential problem into two harmonic oscillators in a new parametric time and quantize this system by using path integrals over holomorphic coordinates of oscillators and derive coherent states. PACS Nos.: 31.15-p, 03.65Ca, 03.65Ge

scholarly journals COHERENT STATES AND GEOMETRIC PHASES IN THE CALOGERO–SUTHERLAND MODEL

2002 ◽  
Vol 17 (02) ◽  
pp. 259-267 ◽  
Author(s):  
DAE-YUP SONG ◽  
JEONGHYEONG PARK
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Periodic Systems ◽  
Classical Solutions ◽  
Geometric Phases ◽  
Sutherland Model ◽  
Inverse Square Potentials ◽  
Time Periodic

Exact coherent states in the Calogero–Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a harmonic oscillator. For quasi-periodic coherent states of the time-periodic systems, geometric phases are evaluated. For the AN-1 Calogero–Sutherland model, the phase is calculated for a general coherent state. The phases for other models are also considered.

scholarly journals Coherent States for the Isotropic and Anisotropic 2D Harmonic Oscillators

2019 ◽  
Vol 1 (2) ◽  
pp. 260-270 ◽  
Author(s):  
James Moran ◽  
Véronique Hussin
Keyword(s):  
Harmonic Oscillator ◽  
Configuration Space ◽  
Coherent States ◽  
Probability Density Functions ◽  
Harmonic Oscillators ◽  
Uncertainty Relations ◽  
Density Functions ◽  
Ladder Operators ◽  
New States ◽  
2D System

In this paper we introduce a new method for constructing coherent states for 2D harmonic oscillators. In particular, we focus on both the isotropic and commensurate anisotropic instances of the 2D harmonic oscillator. We define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the S U ( 2 ) coherent states, where these are then used as the basis of expansion for Schrödinger-type coherent states of the 2D oscillators. We discuss the uncertainty relations for the new states and study the behaviour of their probability density functions in configuration space.

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