Related papers: Effect of the two-parameter generalized Dunkl deri…
In this note we shall continue our study on the initial value problem associated for the generalized derivative Schr\"odinger (gDNLS) equation $$ \partial_tu=i\partial_x^2u + \mu\,|u|^{\alpha}\partial_x u, \hskip10pt x,t\in\mathbb{R},…
We consider the $q$-deformed Schr\"odinger equation of the harmonic oscillator on the $N$-dimensional quantum Euclidian space. The creation and annihilation operator are found, which systematically produce all energy levels and…
The time-dependent quantum system of two laser-driven electrons in a harmonic oscillator potential is analysed, taking into account the repulsive Coulomb interaction between both particles. The Schrodinger equation of the two-particle…
We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\"odinger type and have recently been obtained in \cite{DLS}…
Resonant solutions of the quantum Schr\"odinger equation occur at complex energies where the S-matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schr\"odinger…
In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…
In this paper, we present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$-particle system of Bosons. The interaction potential we consider is given by…
The generalized Moutard transformation of the stationary axially symmetric Schr\"odinger equation is considered. It is shown that a superposition of two Moutard transformations can provide new potentials for the eigenvalue problem. Examples…
This paper investigates a two-dimensional Kemmer oscillator within relativistic quantum mechanics, incorporating minimal length and non-commutative phase space effects. We derive eigen solutions in configuration space $\{p\}$, examining the…
We consider two models where the wave equation can be reduced to the effective Schr\"odinger equation whose potential contains both harmonic and the Coulomb terms, $\omega^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun's…
We generalise the construction of integrals of motion for quantum superintegrable models and the deformed oscillator algebra approach. This is presented in the context of 1D systems admitting ladder operators satisfying a parabosonic…
A novel exactly solvable Schr\"odinger equation with a position-dependent mass (PDM) describing a Coulomb problem in $D$ dimensions is obtained by extending the known duality relating the quantum $d$-dimensional oscillator and…
By substituting the diagonal and the other two adjacent diagonals terms with two different functions depending on two parameters of the discrete Laplacian operator, the nature of its spectrum changes from being purely continuous to…
The extension of dynamical scaling to local, space-time dependent rescaling factors is investigated. For a dynamical exponent $z=2$, the corresponding invariance group is the Schr\"odinger group. Schr\"odinger invariance is shown to…
This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical…
We consider an elastic medium with the distortion of a circular curve into a vertical spiral, and investigate the influence of this topological defect on the doubly anharmonic oscillator. We show that the Schr\"odinger equation for the…
Let $J_\sigma$ be the Dunkl harmonic oscillator on ${\mathbb{R}}$ ($\sigma>-\frac{1}{2}$). For $0<u<1$ and $\xi>0$, it is proved that, if $\sigma>u-\frac{1}{2}$, then the operator $U=J_\sigma+\xi|x|^{-2u}$, with appropriate domain, is…
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y. The singular or caged Dunkl…
We calculate accurate eigenvalues and eigenfunctions of the Schr\"odinger equation for a two-dimensional quantum dipole. This model proved useful for the study of elastic effects of a single edge dislocation. We show that the Rayleigh-Ritz…
Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on 2D quantum problems and present complete treatment on the correspondence including the Schroedinger equation, eigenfunctions and…