Related papers: Partial algebraization and a q-deformed harmonic o…
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…
In the harmonic oscillator representation, the Schrodinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number "n". It is shown that at n>>1 these equations are…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
We consider time-dependent Schr\"{o}dinger equations for a free nonrelativistic particle on the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to these Schr\"{o}dinger equations and show that they form a…
Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known…
We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…
In this paper we study reducibility of time quasiperiodic perturbations of the quantum harmonic or anharmonic oscillator in one space dimension. We modify known algorithms obtaining a reducibility result which allows to deal with…
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role…
With the aim to construct a dynamical model with quantum group symmetry, the $q$-deformed Schr\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space is investigated. After reviewing the differential…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
We consider the Dirac $\delta$-function potential problem in general case of deformed Heisenberg algebra leading to the minimal length. Exact bound and scattering solutions of the problem in quasiposition representation are presented. We…
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the…
The quantum version of a non-linear oscillator, previouly analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form $m={(1+\lambda x^2)}^{-1}$ and with a…
Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…
A set of quasi-exactly solvable quantum mechanical potentials associated with the Poeschl-Teller potential, the generalized Poeschl-Teller potential, the Scarf potential, and the harmonic oscillator potential have been studied. Solutions of…
We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting…
The various relations between $q$-deformed oscillators algebras and the $q$-deformed $su(2)$ algebras are discussed. In particular, we exhibit the similarity of the $q$-deformed $su(2)$ algebra obtained from $q$-oscillators via Schwinger…