Related papers: Second Order Superintegrable Systems in Three Dime…
In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1/2 (neutron) in the field of linear current. Here we present its generalization for any spin which preserves superintegrability. The dynamical…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
In this work we consider superintegrable systems in the classical $r$-matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems with rational potentials from geodesic motion on $R^{2n}$.
The superintegrability of four Hamiltonians $\tilde{H_r} = \lambda\, H_r$, $r=a,b,c,d$, where $H_r$ are known Hamiltonians and $\lambda$ is a certain function defined on the configuration space and depending of a parameter $\kappa$, is…
An overview of maximally superintegrable classical Hamitonians on spherically symmetric spaces is presented. It turns out that each of these systems can be considered either as an oscillator or as a Kepler-Coulomb Hamiltonian. We show that…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…
A quantum sl(2,R) coalgebra is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the non-constant curvature analogues of the spherical, hyperbolic and (anti-)de Sitter spaces.…
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
The quantum $H_3$ integrable system is a 3D system with rational potential related to the non-crystallographic root system $H_3$. It is shown that the gauge-rotated $H_3$ Hamiltonian as well as one of the integrals, when written in terms of…
Quantum semitoric systems form a large class of quantum Hamiltonian integrable systems with circular symmetry which has received great attention in the past decade. They include systems of high interest to physicists and mathematicians such…
It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle.…
New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the…
Carter constant is a non-trivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system…
Several examples of classical superintegrable systems in two-dimensional spac are shown to possess hidden symmetries leading to their linearization. They are those determined 50 years ago in [Phys. Lett. 13, 354 (1965)], and the more recent…
Two-dimensional quantum models which obey the property of shape invariance are built in the framework of polynomial two-dimensional SUSY Quantum Mechanics. They are obtained using the expressions for known one-dimensional shape invariant…