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.

scholarly journals Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Pasquale Bosso ◽  
Giuseppe Gaetano Luciano
Keyword(s):  
Harmonic Oscillator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Heisenberg Algebra ◽  
Quantum Field ◽  
Exact Form ◽  
Ladder Operators ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

AbstractSeveral models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

scholarly journals SOME CONSEQUENCES OF A GENERALIZATION TO HEISENBERG ALGEBRA IN QUANTUM ELECTRODYNAMICS

2003 ◽  
Vol 12 (09) ◽  
pp. 1687-1692 ◽  
Author(s):  
A. CAMACHO
Keyword(s):  
Uncertainty Principle ◽  
Quantum Electrodynamics ◽  
Uncertainty Relation ◽  
Heisenberg Algebra ◽  
Heisenberg Uncertainty Relation ◽  
Fundamental Part ◽  
Heisenberg Uncertainty

In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal observable length), as a fundamental part of the quantization process of the electrodynamical field, renders states in which the uncertainties in the two quadrature components violate the usual Heisenberg uncertainty relation. Hence in this context it may be asserted that any physically realistic generalization of the uncertainty principle must include, not only a minimal observable length, but also a minimal observable momentum.

Generalized two-mode harmonic oscillator: dynamical group and squeezed states

1996 ◽  
Vol 29 (23) ◽  
pp. 7545-7560 ◽  
Author(s):  
José M Cerveró ◽  
Juan D Lejarreta
Keyword(s):  
Harmonic Oscillator ◽  
Squeezed States ◽  
Dynamical Group

Photon added coherent states of the parity deformed oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950104 ◽  
Author(s):  
A. Dehghani ◽  
B. Mojaveri ◽  
S. Amiri Faseghandis
Keyword(s):  
Coherent States ◽  
Uncertainty Relation ◽  
Annihilation Operator ◽  
Single Mode ◽  
Heisenberg Algebra ◽  
Uncertainty Relations ◽  
Deformed Oscillator ◽  
Cat States ◽  
Poissonian Statistics ◽  
Creation Operators

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

scholarly journals Klein–Gordon particle near RN black hole, generalized sl(2) algebra and harmonic oscillator energy

2019 ◽  
Vol 34 (31) ◽  
pp. 1950196
Author(s):  
J. Sadeghi ◽  
M. R. Alipour
Keyword(s):  
Differential Equation ◽  
Information Theory ◽  
Black Hole ◽  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Three Dimensional ◽  
The Other ◽  
Thermodynamical Properties ◽  
Heun Functions ◽  
Klein Gordon

In this paper, we consider Klein–Gordon particle near Reissner–Nordström black hole. The symmetry of such a background led us to compare the corresponding Laplace equation with the generalized Heun functions. Such relations help us achieve the generalized [Formula: see text] algebra and some suitable results for describing the above-mentioned symmetry. On the other hand, in case of [Formula: see text], which is near the proximity black hole, we obtain the energy spectrum. When we compare the equation of RN background with Laguerre differential equation, we show that the obtained energy spectrum is same as the three-dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the RN black hole.

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.

Quantum algebras and parity-dependent spectra

2007 ◽  
Vol 463 (2086) ◽  
pp. 2415-2427 ◽  
Author(s):  
C.V Sukumar ◽  
Andrew Hodges
Keyword(s):  
Quantum Optics ◽  
Harmonic Oscillator ◽  
Combinatorial Theory ◽  
Squeezed States ◽  
Quantum Algebras ◽  
Matrix Elements ◽  
Euler Numbers ◽  
Simple Harmonic Oscillator ◽  
Non Gaussian ◽  
Special Case

We study the structure of a quantum algebra in which a parity-violating term modifies the standard commutation relation between the creation and annihilation operators of the simple harmonic oscillator. We discuss several useful applications of the modified algebra. We show that the Bernoulli and Euler numbers arise naturally in a special case. We also show a connection with Gaussian and non-Gaussian squeezed states of the simple harmonic oscillator. Such states have been considered in quantum optics. The combinatorial theory of Bernoulli and Euler numbers is developed and used to calculate matrix elements for squeezed states.

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