33 citations · 128 across the 15 of their papers we have counts for
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Quadratic symmetry algebras and Sturm algebraization of superintegrable systems with magnetic fields
Shams Ara, Md Fazlul Hoque, Ian Marquette
We study two three-dimensional quantum superintegrable systems in nonvanishing axially symmetric magnetic fields. For each model the integrals generate a quadratic algebra with a C…
New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases
Md Fazlul Hoque, Ondřej Kubů, Antonella Marchesiello +1
We study quadratic integrability of systems with velocity dependent potentials in three-dimensional Euclidean space. Unlike in the case with only scalar potential, quadratic integr…
The \Z2 graded algebra and its irreducible representations
Fahad Sameer Alshammari, Md Fazlul Hoque, Jambulingam Segar
In this paper, we construct finite dimensional irreducible representations for two different versions of \Z2 graded algebra based on eight- and ten-generators. We find t…
Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields
Md Fazlul Hoque, Libor Šnobl
In this paper we present the construction of all nonstandard integrable systems in magnetic fields whose integrals have leading order structure corresponding to the case (i) of The…
Quadratic symmetry algebras and spectrum of the 3D nondegenerate quantum superintegrable system
Mohasena Ahamed, Md Fazlul Hoque
In this paper, we present the quadratic associative symmetry algebra of the 3D nondegenerate maximally quantum superintegrable system. This is the complete symmetry algebra of the…
-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra
Francisco Correa, Md Fazlul Hoque, Ian Marquette +1
The -dimensional Smorodinsky-Winternitz system is a maximally superintegrable and exactly solvable model, being subject of study from different approaches. The model has been de…
Superintegrable systems, polynomial algebra structures and exact derivations of spectra
Md Fazlul Hoque
Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and con…
On superintegrable monopole systems
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to a…
Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
Md Fazlul Hoque, Ian Marquette, Sarah Post +1
We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the…
Quadratic algebra for superintegrable monopole system in a Taub-NUT space
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger…
Recurrence approach and higher rank cubic algebras for the -dimensional superintegrable systems
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
By applying the recurrence approach and coupling constant metamorphosis, we construct higher order integrals of motion for the Stackel equivalents of the -dimensional superinteg…
Family of -dimensional superintegrable systems and quadratic algebra structures
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide appl…
A new family of dimensional superintegrable double singular oscillators and quadratic algebra
Md Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We introduce a new family of -dimensional quantum superintegrable model consisting of double singular oscillators of type . The special cases and were p…
Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension
Md. Fazlul Hoque, Ian Marquette, Yao-Zhong Zhang
We introduce a new superintegrable Kepler-Coulomb system with non-central terms in -dimensional Euclidean space. We show this system is multiseparable and allows separation of v…