scholarly journals Harmonic oscillator with minimal length uncertainty relations and ladder operators

2003 ◽  
Vol 67 (8) ◽  
Author(s):  
Ivan Dadić ◽  
Larisa Jonke ◽  
Stjepan Meljanac
Keyword(s):  
Harmonic Oscillator ◽  
Minimal Length ◽  
Uncertainty Relations ◽  
Ladder Operators

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.

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

EXOTIC REPRESENTATIONS OF THE ISOTROPIC HARMONIC OSCILLATOR

1998 ◽  
Vol 13 (19) ◽  
pp. 3347-3360
Author(s):  
LUIS J. BOYA ◽  
ERIC CHISOLM ◽  
S. M. MAHAJAN ◽  
E. C. G. SUDARSHAN
Keyword(s):  
Harmonic Oscillator ◽  
Rotation Group ◽  
Continuous Family ◽  
Ladder Operators ◽  
Standard Representation ◽  
Isotropic Harmonic Oscillator

We contruct and study a continuous family of representations of the N-dimensional isotropic harmonic oscillator (N≥2) which are not unitarily equivalent to the standard one. We explain why such representations exist and we investigate their simpler properties: the spectrum of the Hamiltonian (which contains nonstandard values), the form of the energy eigenfunctions, and their behavior under the ladder operators. Various symmetry and dynamical groups (e.g. the rotation group) which are valid on the standard representation are not implemented on the new ones. We comment very briefly on the prospects of observing these representations experimentally.

Coherent and squeezed states for the 3D harmonic oscillator

2017 ◽  
Vol 31 (03) ◽  
pp. 1750019
Author(s):  
Amel Mazouz ◽  
Mustapha Bentaiba ◽  
Ali Mahieddine
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Three Dimensional ◽  
Heisenberg Algebra ◽  
Squeezed States ◽  
Ladder Operators ◽  
Compression Effect ◽  
Precise Knowledge ◽  
Generalized Coherent States ◽  
Heisenberg Uncertainty

A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.

UNCERTAINTY RELATIONS FOR THE TIME-DEPENDENT SINGULAR OSCILLATOR

2006 ◽  
Vol 20 (10) ◽  
pp. 1211-1231 ◽  
Author(s):  
J. R. CHOI ◽  
I. H. NAHM
Keyword(s):  
Harmonic Oscillator ◽  
Excited States ◽  
Ground State ◽  
Coherent States ◽  
System Approach ◽  
Uncertainty Relation ◽  
Time Dependent ◽  
Uncertainty Relations ◽  
Number State ◽  
State Uncertainty

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

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