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AN ALGEBRAIC APPROACH TO THE q-DEFORMED MORSE POTENTIAL

Mohammad Reza Setare, O. Hatami

We have obtained the creation and annihilation operators directly from the eigenfunction for the general deformed morse potential in one-dimensional Klein–Gordon equation with equally mixed vector and scalar potentials and also in the Schrödinger equation, we show that these operators satisfy the commutation relation of the SU(1, 1) group. Then we have expressed the Hamiltonian in terms of the su(1, 1) algebra.

Modern Physics Letters AFeb 20, 20099 citations

Duffin-Kemmer-Petiau equation under Hartmann ring-shaped potential

HASSAN HASSANABADI, Mehdi Kamali, Z. Molaee +1 more

We solve the Duffin-Kemmer-Petiau (DKP) equation in the presence of Hartmann ring-shaped potential in (3+1)-dimensional space-time. We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov (NU) method.

Chinese Physics CMar 1, 20140 citations

Duffin-Kemmer-Petiau Oscillator with Spin Non-Commutativity

M’hamed Hadj Moussa

International Journal of Theoretical PhysicsOct 9, 20235 citations

Fock representations of Q-deformed commutation relations

Marek Bożejko, Eugene Lytvynov, Janusz Wysoczański

We consider Fock representations of the Q-deformed commutation relations ∂s∂t†=Q(s,t)∂t†∂s+δ(s,t) for s,t∈T. Here T:=Rd (or more generally T is a locally compact Polish space), the function Q:T2→C satisfies |Q(s,t)|≤1 and Q(s,t)=Q(t,s)¯, and ∫T2h(s)g(t)δ(s,t) σ(ds)σ(dt):=∫Th(t)g(t) σ(dt), σ being a fixed reference measure on T. In the case, where |Q(s,t)|≡1, the Q-deformed commutation relations describe a generalized statistics studied by Liguori and Mintchev. These generalized statistics contain anyon statistics as a special case (with T=R2 and a special choice of the function Q). The related Q-deformed Fock space F(H) over H:=L2(T→C,σ) is constructed. An explicit form of the orthogonal projection of H⊗n onto the n-particle space Fn(H) is derived. A scalar product in Fn(H) is given by an operator Pn≥0 in H⊗n which is strictly positive on Fn(H). We realize the smeared operators ∂t† and ∂t as creation and annihilation operators in F(H), respectively. Additional Q-commutation relations are obtained between the creation operators and between the annihilation operators. They are of the form ∂s†∂t†=Q(t,s)∂t†∂s†, ∂s∂t=Q(t,s)∂t∂s, valid for those s,t∈T for which |Q(s, t)| = 1.We consider Fock representations of the Q-deformed commutation relations ∂s∂t†=Q(s,t)∂t†∂s+δ(s,t) for s,t∈T. Here T:=Rd (or more generally T is a locally compact Polish space), the function Q:T2→C satisfies |Q(s,t)|≤1 and Q(s,t)=Q(t,s)¯, and ∫T2h(s)g(t)δ(s,t) σ(ds)σ(dt):=∫Th(t)g(t) σ(dt), σ being a fixed reference measure on T. In the case, where |Q(s,t)|≡1, the Q-deformed commutation relations describe a generalized statistics studied by Liguori and Mintchev. These generalized statistics contain anyon statistics as a special case (with T=R2 and a special choice of the function Q). The related Q-deformed Fock space F(H) over H:=L2(T→C,σ) is constructed. An explicit form of the orthogonal projection of H⊗n onto the n-particle space Fn(H) is derived. A scalar product in Fn(H) is given by an operator Pn≥0 in H⊗n which is strictly positive on Fn(H). We realize the smeared operators ∂t† and ∂t as creation and annihilation operators in F(H), respectively. Additional Q-commutation relations are obtained between the creation operators and between the annihilation operators. They are of the form ∂s†∂t†=Q(t,s)∂t†∂s†, ∂s∂t=Q(t,s)∂t∂s, valid for those s,t∈T for which |Q(s, t)| = 1.

arXiv:1603.03075Journal of Mathematical PhysicsJul 1, 201711 citations

The relativistic Duffin–Kemmer–Petiau sextic oscillator

F. Yasuk, M. Karakoç, Ismail Boztosun

In this study, we construct the deformed form of the relativistic Duffin–Kemmer–Petiau (DKP) oscillator including a term qr 3 . The DKP oscillator with a deformed term becomes the radial sextic oscillator in the non-relativistic limit. The DKP sextic oscillator problem is solved numerically within the framework of the asymptotic iteration method. We present the energy eigenvalues for the ground and excited states.

Physica ScriptaOct 1, 200821 citations

DKP Equation in the q-deformed Quantum Mechanics

Hadi Sobhani, HASSAN HASSANABADI, Won Sang Chung

Few-Body SystemsApr 12, 20231 citation

Morse potential of the q-deformed in the Duffin–Kemmer–Petiau equation

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Morse potential of the q-deformed in the Duffin–Kemmer–Petiau equation

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