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

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.

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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

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Molecular Coherent States for a Generalized Morse Oscillator*

Zeitschrift für Physikalische Chemie ◽

10.1524/zpch.1996.1.1.051 ◽

1996 ◽

Vol 1 (1) ◽

pp. 51-56 ◽

Cited By ~ 1

Author(s):

G. E. Drǎgǎnescu ◽

N. M. Avram

Keyword(s):

Coherent States ◽

Morse Oscillator

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COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA

Modern Physics Letters A ◽

10.1142/s0217732309030722 ◽

2009 ◽

Vol 24 (25) ◽

pp. 2039-2051 ◽

Cited By ~ 2

Author(s):

H. FAKHRI ◽

B. MOJAVERI ◽

A. DEHGHANI

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Heisenberg Algebra ◽

Creation And Annihilation Operators ◽

Number Of Generators ◽

Simple Harmonic Oscillator

We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with [Formula: see text] and [Formula: see text] symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are [Formula: see text]-pseudo-Hermiticity and [Formula: see text]-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

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Eigenstates, coherent states, and uncertainty products for the Morse oscillator

Physical Review A ◽

10.1103/physreva.19.438 ◽

1979 ◽

Vol 19 (2) ◽

pp. 438-444 ◽

Cited By ~ 126

Author(s):

Michael Martin Nieto ◽

L. M. Simmons

Keyword(s):

Coherent States ◽

Morse Oscillator

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EIGENSTATES OF LINEAR COMBINATIONS OF TWO-BOSON CREATION AND ANNIHILATION OPERATORS: AN ALGEBRAIC APPROACH

Modern Physics Letters A ◽

10.1142/s021773239600237x ◽

1996 ◽

Vol 11 (29) ◽

pp. 2381-2396 ◽

Cited By ~ 6

Author(s):

P. SHANTA ◽

S. CHATURVEDI ◽

V. SRINIVASAN

Keyword(s):

Closed Form ◽

Coherent States ◽

Algebraic Approach ◽

Squeezed States ◽

Linear Combinations ◽

Creation And Annihilation Operators

Eigenstates of the linear combinations a2+βa†2 and ab+βa†b†of two-boson creation and annihilation operators are presented. The algebraic procedure given here is based on the work of Shanta et al. [Phys. Rev. Lett.72, 1447, (1994)] for constructing eigenstates of generalized annihilation operators. Expressions for the overlaps of these states with the number states, the coherent states and the squeezed states are given in a closed form.

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