UNCERTAINTY RELATIONS FOR A DEFORMED OSCILLATOR

We construct a deformed oscillator whose energy spectra is similar to that of a Morse potential. We obtain a convenient algebraic representation of the displacement and the momentum of a Morse oscillator by expanding them in terms of deformed creation and annihilation operators and we compute their average values between approximate coherent states of the deformed oscillator, and we compare them to the results obtained using the exact Morse coordinate and momenta. Finally we evaluate the temporal evolution of the dispersion (Δx)(Δp) and show that these states are not minimum uncertainty states.

Download Full-text

Photon added coherent states of the parity deformed oscillator

Modern Physics Letters A ◽

10.1142/s0217732319501049 ◽

2019 ◽

Vol 34 (14) ◽

pp. 1950104 ◽

Cited By ~ 4

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.

Download Full-text

Creation and annihilation operators for the Morse oscillator and the coherent states

Canadian Journal of Physics ◽

10.1139/cjp-76-4-273 ◽

1998 ◽

Vol 76 (4) ◽

pp. 273-281 ◽

Cited By ~ 1

Author(s):

Gh.E. Dr. E. Draganescu ◽

N.M. Avram

Keyword(s):

Coherent States ◽

Morse Oscillator ◽

Creation And Annihilation Operators

Download Full-text

DEFORMED HARMONIC OSCILLATOR FOR NON-HERMITIAN OPERATOR AND THE BEHAVIOR OF PT AND CPT SYMMETRIES

International Journal of Modern Physics B ◽

10.1142/s0217979206034698 ◽

2006 ◽

Vol 20 (16) ◽

pp. 2313-2322 ◽

Cited By ~ 1

Author(s):

A. JANNUSSIS ◽

K. VLACHOS ◽

V. PAPATHEOU ◽

A. STREKLAS

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Hermitian Operator ◽

Uncertainty Relations ◽

Complex Spectrum ◽

Cpt Symmetry ◽

Solid State Physics ◽

Special Values ◽

Deformed Oscillator ◽

Positive Spectrum

In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator [Formula: see text] where λ,θ are real positive parameters, since the parameters α,β,m are for the general case complex. For the case α=1,β=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators [Formula: see text] in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex α=1,β=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case α,β,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters α,β the spectrum is real discrete and positive and the CPT symmetry is preserved. The general problem of deformed oscillator for non hermitian operators can be applied to the Solid State Physics.

Download Full-text

The Uncertainty Principle Derived by The Finite Transmission Speed of Light and Information

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v3i3.2059 ◽

2014 ◽

Vol 3 (3) ◽

pp. 257-266 ◽

Cited By ~ 1

Author(s):

Piero Chiarelli

Keyword(s):

Uncertainty Principle ◽

Large Scale ◽

Uncertainty Relations ◽

Speed Of Light ◽

Energy Fluctuation ◽

Hydrodynamic Analogy ◽

Non Local ◽

Minimum Uncertainty ◽

Quantum Hydrodynamic ◽

Transmission Speed

This work shows that in the frame of the stochastic generalization of the quantum hydrodynamic analogy (QHA) the uncertainty principle is fully compatible with the postulate of finite transmission speed of light and information. The theory shows that the measurement process performed in the large scale classical limit in presence of background noise, cannot have a duration smaller than the time need to the light to travel the distance up to which the quantum non-local interaction extend itself. The product of the minimum measuring time multiplied by the variance of energy fluctuation due to presence of stochastic noise shows to lead to the minimum uncertainty principle. The paper also shows that the uncertainty relations can be also derived if applied to the indetermination of position and momentum of a particle of mass m in a quantum fluctuating environment.

Download Full-text

A simple algebraic approach to coherent states for the Morse oscillator

Journal of Physics A General Physics ◽

10.1088/0305-4470/25/6/022 ◽

1992 ◽

Vol 25 (6) ◽

pp. 1671-1683 ◽

Cited By ~ 48

Author(s):

I L Cooper

Keyword(s):

Coherent States ◽

Algebraic Approach ◽

Morse Oscillator

Download Full-text

Rotational excitations of diatomic molecule with delta potential barrier

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633618500220 ◽

2018 ◽

Vol 17 (04) ◽

pp. 1850022

Author(s):

Sonia Lumb ◽

Shalini Lumb ◽

Vinod Prasad

Keyword(s):

Diatomic Molecule ◽

Applied Field ◽

Morse Potential ◽

Short Range ◽

Delta Function ◽

Energy Spectra ◽

Matrix Elements ◽

Delta Potential ◽

Homonuclear Diatomic Molecule ◽

Delta Functions

The interatomic interactions in a diatomic molecule can be fairly modeled by the Morse potential. Short range interactions of the molecule with the neighboring environment can be analyzed by modifying this potential by delta functions. Energy spectra and radial matrix elements have been calculated using an accurate nine-point finite-difference method for such an interacting homonuclear diatomic molecule. The effect of the strength and position of a single delta function interaction on the alignment of this molecule has been studied. The dependence of alignment on the strength of applied field has also been analyzed.

Download Full-text