The q-deformed harmonic oscillator, coherent states, and the uncertainty relation
V. V. Eremin,A. A. Meldianov +1 more
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For a q-deformed harmonic oscillator, the product of the coordinate-momentum uncertainties in q-oscillator eigenstates and coherent states was shown in this paper.Abstract:
For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We calculate the product of the “coordinate-momentum” uncertainties in q-oscillator eigenstates and in coherent states. For the oscillator, this product is minimum in the ground state and equals 1/2, as in the standard quantum mechanics. For coherent states, the q-deformation results in a violation of the standard uncertainty relation; the product of the coordinate-and momentum-operator uncertainties is always less than 1/2. States with the minimum uncertainty, which tends to zero, correspond to the values of λ near the convergence radius of the q-exponential.read more
Citations
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q -Difference Equations
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TL;DR: In this article, a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-booms.
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TL;DR: In this paper, the Hamiltonian of Dirac oscillator in an external magnetic field in terms of q-deformed creation and annihilation operators in 2 + 1 dimensions was obtained, eigenvalues and eigenfunctions were derived.
References
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TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.
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TL;DR: In this article, a new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and qanalogues to the Wigner and Racah operators.
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Uncertainty relation in quantum mechanics with quantum group symmetry
TL;DR: In this article, the commutation relations, uncertainty relations, and spectra of position and momentum operators were studied within the framework of quantum group symmetric Heisenberg algebras and their (Bargmann) Fock representations.
Journal ArticleDOI
On the q oscillator and the quantum algebra suq(1,1)
P. P. Kulish,E. V. Damaskinsky +1 more
TL;DR: In this paper, different q bosonisations of the quantum suq(1,1) algebra are given and the corresponding infinite dimensional representations of discrete series are analysed, and some problems of the q-deformed harmonic oscillator are discussed.
Journal ArticleDOI
Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
TL;DR: In this article, the authors studied the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations.