Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Miller Jr., Willard"'
In this paper, we point out connections between certain types of indecomposable representations of $sl(2)$ and generalizations of well-known orthogonal polynomials. Those representations take the form of infinite dimensional chains of weight or gener
Externí odkaz:
http://arxiv.org/abs/2309.02667
Publikováno v:
Journ of Math Physics 62, 072103 (2021)
As a generalization and extension of our previous paper {\it J. Phys. A: Math. Theor. 53 055302} \cite{AME2020}, in this work we study a quantum 4-body system in $\mathbb{R}^d$ ($d\geq 3$) with quadratic and sextic pairwise potentials in the {\it rel
Externí odkaz:
http://arxiv.org/abs/2103.08094
Publikováno v:
Int.Journ.Mod.Phys. A36(18) (2021) 2150140
We consider the classical 3-body system with $d$ degrees of freedom $(d>1)$ at zero total angular momentum. The study is restricted to potentials $V$ that depend solely on relative (mutual) distances $r_{ij}=\mid {\bf r}_i - {\bf r}_j\mid$ between bo
Externí odkaz:
http://arxiv.org/abs/2007.11959
Publikováno v:
Journal of Physics A: Mathematical and Theoretical 53 (49) 494003 1-21 (2020)
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schr\"odinger eigenvalue equation $H\Psi \equiv (\Delta_2 +V)\Psi=E\Psi$ on any 2D Riemannian manifold, real or
Externí odkaz:
http://arxiv.org/abs/2006.15677
Publikováno v:
SIGMA 16 (2020), 135, 33 pages
We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex Euclidean space.
Externí odkaz:
http://arxiv.org/abs/2004.00933
Publikováno v:
Journal of Physics A54 (2021) 015204
It is shown that planar quantum dynamics can be related to 3-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the $O(d)$ symmetry reduction from $d$ degrees of freedom to one degre
Externí odkaz:
http://arxiv.org/abs/1912.05726
Publikováno v:
J. Phys. A: Math. Theor. 53 (2020) 055302 (25pp)
In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative distances, $|{\bf r}_i - {\bf r}_j |$, between particles. The two-body harmonic oscillator is two-parametric and can be reduced to
Externí odkaz:
http://arxiv.org/abs/1909.11708
Publikováno v:
Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, 111-120 (2021)
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schr\"odinger eigenvalue equation $H\Psi \equiv (\Delta_2 +V)\Psi=E\Psi$ on any 2D Riemannian manifold, real or
Externí odkaz:
http://arxiv.org/abs/1909.08654
Publikováno v:
Journ of Math Physics A60 (2019) 062101
Due to its great importance for applications, we generalize and extend the approach of our previous papers to study aspects of the quantum and classical dynamics of a $4$-body system with equal masses in {\it $d$}-dimensional space with interaction d
Externí odkaz:
http://arxiv.org/abs/1811.06008
Publikováno v:
Journal of Physics A51 (2018) 205201
We employ generalized Euler coordinates for the $n$ body system in $d \geq n-1$ dimensional space, which consists of the centre-of-mass vector, relative (mutual), mass-independent distances $r_{ij}$ and angles as remaining coordinates. We prove that
Externí odkaz:
http://arxiv.org/abs/1709.01108