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Andreas Ruffing

Publications and source records attributed to Andreas Ruffing.

7 recordsLinked to original sources
arXiv2025

Oganesson versus Uranium Hydrogen-like Ions and Beyond (from the Viewpoint of Old Quantum Mechanics)

We compare, within the framework of the old Bohr-Sommerfeld atomic model, Uranium (Z=92) versus hypothetical Oganesson (Z=118) relativistic hydrogen-like ions and beyond. Existence of a self-intersecting orbit in the super strong static Coulomb field is demonstrated with the aid of Mathematica computer algebra system. A possibility of a similar 'Oganesson-type' effect in a strong gravitational field is also mentioned. Appearance of a multi self-intersecting trajectory is demonstrated in a hypothetical Unbibium, an element with Z = 122, and beyond with Z< 136. A topological classification of the strength for Coulomb fields in the superheavy transuranium elements may be given in terms of the 'winding' numbers.

quant-ph↗
arXiv2025

Old Quantum Mechanics by Bohr and Sommerfeld from a Modern Perspective

We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are evaluated by elementary techniques, and connections with the Schr\"{o}dinger and Dirac equations are established. Historical developments and key transitions from classical to quantum theory are discussed to clarify the structure and significance of the old quantum mechanics.

quant-ph↗
arXiv2005

Some cubic birth and death processes and their related orthogonal polynomials

The orthogonal polynomials with recurrence relation \[(\la\_n+μ\_n-z) F\_n(z)=μ\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z)\] with two kinds of cubic transition rates $\la\_n$ and $μ\_n,$ corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes of polynomials, which enable us to compute their Nevanlinna matrices. We discuss the asymptotics of the Nevanlinna matrices in the complex plane.

math-ph↗
arXiv1997

The First Moment of delta g(x) -- a Comparative Study

The sensititivity of various future polarization experiments to the first moment Delta g of the polarized gluon density is elucidated in detail. It is shown to what extent the first moment can be extracted from the future data as compared to the higher moments. We concentrate on two processes which in the near future will become an important source of information on the polarized gluon density, namely the photoproduction of open charm to be studied at CERN (COMPASS) and SLAC and the production of direct photons at RHIC.

hep-ph↗
arXiv1992

String branchings and complex tori and algebraic representations of generalized Krichever-Novikov algebras

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b-c systems. The defining cocycle for this central extension deforms to the well known Virasoro cocycle for certain kinds of degenerations of the torus. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40

hep-th↗
arXiv1992

String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b-c systems. The defining cocycle for this central extension deforms to the well known Virasoro cocycle for certain kinds of degenerations of the torus. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40

alg-geom↗