Related papers: Minimal Length Uncertainty Relation and Hydrogen A…
Nuclear deformation effects are theoretically investigated in terms of deformation corrections of the electronic binding and transition energies, $g$ factor, and hyperfine splitting constant. By solving the Dirac equation twice, with the…
We present a description of a new kind of the deformed canonical commutation relations, their representations and generated by them Heisenberg-Weyl algebra. This deformed algebra allows us to derive operations of the Hopf algebra structure:…
In this paper we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one dimensional case, the existence…
Energy spectrum of isotropic oscillator as a function of noncommutativity parameter theta is studied. It is shown that for a dense set of values of theta the spectrum is degenerated and the algebra responsible for degeneracy can be always…
A variant of energy scale deformation is considered for the S = 1/2 antiferromagnetic Heisenberg model on polyhedra. The deformation is induced by the perturbations to the uniform Hamiltonian, whose coefficients are determined by the bond…
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not…
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…
We investigated the elastic scattering problem with deformed Heisenberg algebra leading to the existence of a minimal length. The continuity equations for the moving particle in deformed space were constructed. We obtained the Green's…
We consider the consequences of the presence of metric fluctuations upon the properties of a hydrogen atom. Particularly, we introduce these metric fluctuations in the corresponding effective Schroedinger equation and deduce the…
We develop a semiclassical theory for the spectral rigidity of non-hydrogenic Rydberg atoms in electric fields and evaluate the significant deviations from the well-known Poissonian behaviour in the hydrogenic case. The resulting formula is…
We investigate the consequences of one extra compactified dimension for the energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$ in non-compactified 4d space. The…
We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation,…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…
A detailed analysis of the bremsstrahlung spectrum at nonrelativistic electron scattering on argon and xenon is carried out. It is shown that the approximate formulas widely used for the description of bremsstrahlung spectra lead to…
We study space-time non-commutativity applied to the hydrogen atom via the Seiberg-Witten map and its phenomenological effects. We find that it modifies the Coulomb potential in the Hamiltonian and add an r-3 part. By calculating the…
We investigated the orbital magnetic moment of electron in the hydrogen atom in deformed space with minimal length. It turned out that corrections to the magnetic moment caused by deformation depend on one parameter in the presence of…
We investigate the holographic bound utilizing a homogeneous, isotropic, and non-relativistic neutral hydrogen gas present in the de Sitter space. Concretely, we propose to employ de Sitter holography intertwined with quantum deformation of…
In this paper we introduce the $q$-deformed Heisenberg picture equation. We consider some examples such as : the spinless particle, the electr\'on interaction with a magnnetic field and $q$-deformed harmonnic oscillator. The $q$-Heisenberg…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…