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Bouncing non-singular isotropic cosmological solutions are investigated in a simple model of scalar-tensor gravity. New families of such solutions are found and their properties are presented and analyzed using an effective potential as the…
Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends…
Bound-state solutions of the singular harmonic oscillator and singular Coulomb potentials in arbitrary dimensions are generated in a simple way from the solutions of the one-dimensional generalized Morse potential. The nonsingular harmonic…
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.…
A new exactly solvable case in strong-field quantum electrodynamics with a time-dependent external electric field is presented. The corresponding field is given by an analytic function, which is asymmetric (in contrast to Sauter-like…
The differential realization of the potential group SO(2,2) is used. The spectrum-generating algebra for a kind of exactly solvable potentials endowed with position-dependent mass is constructed.
A gamma-rigid solution of the Bohr Hamiltonian is derived for gamma=0 utilizing the Davidson potential in the beta variable. This solution is going to be called X(3)-D. The energy eigenvalues and wave functions are obtained by using an…
The energy eigenvalues and the wave functions of an $\alpha$ particle in a Bohrium $270$ nucleus were calculated by solving Schr\"odinger equation for Generalized Symmetric Woods-Saxon potential. Using the energy spectrum by excluding and…
We propose two generalisations of the Coulomb potential equation of quantum mechanics and investigate the occurence of algebraic eigenfunctions for the corresponding Scrh\"odinger equations. Some relativistic counterparts of these problems…
The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component…
We investigate the presence of non-topological solutions of the Q-ball type in (1, 1) spacetime dimensions. The model engenders the global U(1) symmetry and is of the k-field type, since it contains a new term, of the fourth-order power in…
A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schro\"edinger equation in momentum representation on the case of deformed Heisenberg…
A solution of the Bohr collective hamiltonian for the $\beta-$soft, $\gamma-$soft triaxial rotor with $\gamma \sim \pi/6$ is presented making use of a harmonic potential in $\gamma$ and Coulomb-like and Kratzer-like potentials in $\beta$.…
We consider the Schr{\"o}dinger equation with a nondispersive logarithmic nonlinearity and a repulsive harmonic potential. For a suitable range of the coefficients, there exist two positive stationary solutions, each one generating a…
We found hermitian realizations of the position vector $\vec{r}$, the angular momentum $\vec{\Lambda}$ and the linear momentum $\vec{p}$, all behaving like vectors under the $su_q(2)$ algebra, generated by $L_0$ and $L_\pm$. They are used…
We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein's equations with a positive cosmological constant and conformally coupled scalar field. The neutral black holes are always…
It is shown that an extended q-deformed $su(2)$ algebra with an extra (``Schwinger '') term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch…
We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are…
An analytic, parameter-free (up to overall scale factors) solution of the Bohr Hamiltonian involving axially symmetric quadrupole and octupole deformations, as well as an infinite well potential, is obtained, after separating variables in a…
This paper deals with the partial solution of the energy-eigenvalue problem for one-dimensional Schr\"odinger operators of the form $H_N=X_0^2+V_N$, where $V_N=X_N^2+\alpha X_{N-1}$ is a polynomial potential of degree $(2N-2)$ and $X_i$ are…