Zobrazeno 1 - 10
of 108
pro vyhledávání: '"Szmytkowski, Radosław"'
Autor:
Szmytkowski, Radosław
A Schr\"odinger particle on an $N$-dimensional ($N\geqslant2$) hypersphere of radius $R$ is considered. The particle is subjected to the action of a force characterized by the potential $V(\theta)=2m\omega_{1}^{2}R^{2}\tan^{2}(\theta/2)+2m\omega_{2}^
Externí odkaz:
http://arxiv.org/abs/2408.10860
Autor:
Szmytkowski, Radosław
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor wave functi
Externí odkaz:
http://arxiv.org/abs/2203.09891
Autor:
Szmytkowski, Radosław
Publikováno v:
Phys. Rev. A 98, 042507 (2018)
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schr\"odinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb
Externí odkaz:
http://arxiv.org/abs/1807.08662
Autor:
Szmytkowski, Radosław
Publikováno v:
Ann. Phys. 401 (2019) 174-92
A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy
Externí odkaz:
http://arxiv.org/abs/1807.07012
Autor:
Szmytkowski, Radosław
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian expansion o
Externí odkaz:
http://arxiv.org/abs/1806.03477
Autor:
Szmytkowski, Radosław
Publikováno v:
Integral Transforms Spec. Funct. 28 (2017) 645-62
We provide closed-form expressions for the degree-derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$ and $[\partial Q_{\nu}(z)/\partial\nu]_{\nu=n}$, with $z\in\mathbb{C}$ and $n\in\mathbb{N}_{0}$, where $P_{\nu}(z)$ and $Q_{\nu}(z)$ are
Externí odkaz:
http://arxiv.org/abs/1707.02417
Publikováno v:
Phys. Rev. A 93, 062502 (2016)
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$-polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Gre
Externí odkaz:
http://arxiv.org/abs/1602.00613
Autor:
Szmytkowski, Radosław
We derive explicit expressions for the parameter derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=0}$ and $[\partial^{3}P_{\nu}(z)/\partial\nu^{3}]_{\nu=0}$, where $P_{\nu}(z)$ is the Legendre function of the first kind. It is found that {d
Externí odkaz:
http://arxiv.org/abs/1301.6586
Autor:
Szmytkowski, Radosław
The Schr\"odinger-Coulomb Sturmian problem in $\mathbb{R}^{N}$, $N\geqslant2$, is considered in the momentum representation. An integral formula for the Gegenbauer polynomials, found recently by Cohl [arXiv:1105.2735], is used to separate out angular
Externí odkaz:
http://arxiv.org/abs/1111.1661