SU(d)-INVARIANT MULTIDIMENSIONAL q-OSCILLATORS WITH BOSONIC DEGENERACY

2000 ◽  
Vol 15 (19) ◽  
pp. 1237-1242 ◽  
Author(s):  
A. ALGIN ◽  
M. ARIK ◽  
N. M. ATAKISHIYEV
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Lie Group ◽  
The Other ◽  
Quantum Harmonic Oscillator ◽  
Standard Quantum ◽  
Newton Equation ◽  
Two Parameter

Multidimensional two-parameter (q1, q2)-oscillators are of two kinds: one is invariant under the (ordinary) Lie group SU (d), whereas the other is invariant under the quantum group SU q(d) where q = q1/q2. It is shown that the q1 = q2 limit of both of these two-parameter oscillators coincide and give the q-deformed Newton oscillator which can be derived from the standard quantum harmonic oscillator Newton equation. The bosonic degeneracies of the excited levels of these oscillators are different for q1 ≠ q2, but coincide in the q1 = q2 limit.

DEFORMED HARMONIC OSCILLATOR AND NONLINEAR COHERENT STATES: NONCOMMUTATIVE QUANTUM SPACE APPROACH

2009 ◽  
Vol 24 (10) ◽  
pp. 1963-1986 ◽  
Author(s):  
MOHAMMAD HOSSEIN NADERI ◽  
MAHMOOD SOLTANOLKOTABI ◽  
RASOUL ROKNIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Differential Calculus ◽  
Quantum Plane ◽  
Quantum Harmonic Oscillator ◽  
Commutation Relations ◽  
Noncommutative Differential Calculus ◽  
Two Parameter ◽  
Noncommutative Quantum ◽  
Space Approach

In this paper, by using the Wess–Zumino formalism of noncommutative differential calculus, we show that the concept of nonlinear coherent states originates from noncommutative geometry. For this purpose, we first formulate the differential calculus on a GL p, q(2) quantum plane. By using the commutation relations between coordinates and their interior derivatives, we then construct the two-parameter (p, q)-deformed quantum phase space together with the associated deformed Heisenberg commutation relations. Finally, by applying the obtained results for the quantum harmonic oscillator we construct the associated coherent states, which can be identified as nonlinear coherent states. Furthermore, we show that some of the well-known deformed (nonlinear) coherent states, such as two-parameter (p, q)-deformed coherent states, Maths-type q-deformed coherent states, Phys-type q-deformed coherent states and Quesne deformed coherent states, can be easily obtained from our treatment.

scholarly journals A New Framework for the Determination of the Eigenvalues and Eigenfunctions of the Quantum Harmonic Oscillator

2021 ◽  
Vol 13 (6) ◽  
pp. 20
Author(s):  
Francis T. Oduro ◽  
Amos Odoom
Keyword(s):  
Harmonic Oscillator ◽  
The Other ◽  
Erential Equation ◽  
Quantum Harmonic Oscillator ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Alternative Approach ◽  
Schmidt Orthogonalization ◽  
New Framework

This study was designed to obtain the energy eigenvalues and the corresponding Eigenfunctions of the Quantum Harmonic oscillator through an alternative approach. Starting with an appropriate family of solutions to a relevant linear di erential equation, we recover the Schr¨odinger Equation together with its eigenvalues and eigenfunctions of the Quantum Harmonic Oscillator via the use of Gram Schmidt orthogonalization process in the usual Hilbert space. Significantly, it was found that there exists two separate sequences arising from the Gram Schmidt Orthogonalization process; one in respect of the even eigenfunctions and the other in respect of the odd eigenfunctions.

scholarly journals The Real Forms of the Fractional Supergroup SL(2,C)

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 933
Author(s):  
Yasemen Ucan ◽  
Resat Kosker
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
The Real ◽  
And Mathematics ◽  
Real Forms

The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL2,C is one of these important groups. There are real forms of the classical Lie group SL2,C and the quantum group SL2,C in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A3NSL2,C, for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A31SL2,C and A32SL2,C.

scholarly journals Quadratic open quantum harmonic oscillator

2020 ◽  
Vol 110 (7) ◽  
pp. 1759-1782
Author(s):  
Ameur Dhahri ◽  
Franco Fagnola ◽  
Hyun Jae Yoo
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Harmonic Oscillator ◽  
Open Quantum
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