Related papers: Shape Invariant Natanzon Potentials from Potential…
We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poisson algebra over an algebraically closed field decomposes…
This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three or more distinct topological sectors, with multiplicity one,…
The equivalence class of absolute configurations of a system under the group of similarity transformations $Sim(3)$ is called the shape of the system. The $Sim(3)$ invariant Lagrangian of the modified Newtonian theory ensures the existence…
We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of $p$ iterations. These cyclic shape invariant potentials enlarge the limited…
An $SO(9,1)$ invariant formulation of an 11-dimensional supermembrane is presented by combining an $SO(10,1)$ invariant treatment of reparametrization symmetry with an $SO(9,1)$ invariant $\theta_{R} = 0$ gauge of $\kappa$-symmetry. The…
We present a collection of matrix valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of the generic form $W=kQ+\frac1k R+P$ where…
We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of so(2n+1). The irreducible representations correspond to the generalized Young diagrams. With respect to this measure the…
A complete system of differential invariants for equivalence of curves in the $n$-dimensional pseudo-euclidean space with respect to the action of each of the groups $K^n \lhd O(n,p,K)$, $K^n \lhd SO(n,p,K)$, $O(n,p,K)$, and $SO(n,p,K)$,…
We develop a structure theory for nilpotent symplectic alternating algebras.
The basic concepts of factorizable problems in one-dimensional Quantum Mechanics, as well as the theory of Shape Invariant potentials are reviewed. The relation of this last theory with a generalization of the classical Factorization Method…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…
A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part…
An appropriateness of a space asymmetry of shape invariant potentials with scaling of parameters and potentials of Shabat and Spiridonov in calculation of their forms, wave functions and discrete energy spectra has proved and has…
We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…
This study delves into the exploration of the limiting shape theorem for subadditive processes on finitely generated groups with polynomial growth, commonly referred to as virtually nilpotent groups. Investigating the algebraic structures…
Shape Theory, together with Shape-and-Scale Theory, comprise Relational Theory. This consists of $N$-point models on a manifold $M$, for which some geometrical automorphism group $G$ is regarded as meaningless and is thus quotiented out…
Let $U$ be either classical or quantized universal enveloping algebra of $\s\l(n+1)$ extended over the field of fractions of the Cartan subalgebra. We suggest a PBW basis in $U$ over the extended Cartan subalgebra diagonalizing the…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
In this manuscript, we present analytical solution of the Klein-Gordon equation with the multi-parameter q-deformed Woods-Saxon type potential energy under the spin symmetric limit in $(1+1)$ dimension. In the scattering case, we obtain the…
We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We…