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Extra Colloquium Mathematics, Prof.dr. A.G. Nikitin (Kiev, IM NAS Ukraine)

12 June 2014

Join us for coffee and tea at 12.45 p.m.

Date:                      

Thursday, June 12th 2014

Speaker:

Prof.dr. A.G. Nikitin (Kiev, IM NAS Ukraine)

Room:

5161.0253 (Bernoulliborg)

Time:

13.00

Title:   Laplace-Runge-Lenz vectors with spin in any dimension.


Abstract:

The Laplace-Runge-Lenz vector (LRLV) is a cornerstone of celestial mechanics. It also plays an important role in quantum mechanics, being an integral of motion for the Hydrogen atom and some other systems. However, models of non-relativistic systems admitting   LRLV usually ignore the spin of orbital particles. A collection of QM systems admitting LRLV vector with spin is presented In this talk. The collection includes 2d and 3d systems with arbitrary spin, as well as systems of arbitrary dimension with spins 0, 1/2, and 1. All these systems are "superintegrable" and they can be solved exactly. Physically speaking, they describe neutral particles with non-trivial multipole momenta (in particular, the neutron). References [1] A. G. Nikitin, Matrix superpotentials and superintegrable systems for arbitrary spin, J. Phys. A: Math. Theor. 45 (2012) 225205 (13p). [2] A. G. Nikitin, New exactly solvable systems with Fock symmetry, J. Phys. A: Math. Theor. 45 (2012) 485204 (9pp). [3] A. G. Nikitin. Integrability and supersymmetry of Schrodinger-Pauli equations for neutral particles. J. Math. Phys. 53, 122103 (2012); http://dx.doi.org/10.1063/1.4768464 (14 pages). [4] A. G. Nikitin. Superintegrable systems with spin invariant with respect to the rotation group. J. Phys. A: Math. Theor. 46 256204 (2013), arXiv 1303.1297 [5] A. G. Nikitin. Laplace-Runge-Lenz vector for arbitrary spin, J. Math. Phys. 54, 123506 (2013); http://dx.doi.org/10.1063/1.4843435 [6] A. G. Nikitin. Superintegrable systems with arbitrary spin. Ukr. J. Phys. 58 No 11, pp. 1046-1054 (2013) [7] A.G Nikitin. Laplace-Runge-Lenz vector with spin in any dimension,arXiv:1403.2867

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
Dr. A.V. Kiselev (e-mail: a.v.kiselev@rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/

Last modified:06 June 2018 2.05 p.m.

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