ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Lie Algebra contractions and Separation of Variables on Two-dimensional Hyperboloids. Basis Functions and Interbasis Expansions.

George S. Pogosyan
Department of Mathematics, University of Guadalajara, Guadalajara Mexico

Thursday, September 29, 2016 15:00-16:00,
Building 225, B111
Thursday, September 29, 2016 13:00-14:00,
Room 4072

Abstract: Olevskiĭ (1950) was the first to show that the two-dimensional Helmholtz equation for the hyperboloid allows separation of the variables in nine orthogonal coordinate systems. Next Smorodinskiĭ, Winternitz and Lukacs (1968) shows that each of the separating coordinate systems associated with the quadratic operator of symmetry L in the enveloping Lie algebra so(2,1). In my report, I will present a complete description of the normalized eigenfunctions of the Helmholtz equation which correspond to a separation of variables on the six systems of coordinates on a two-dimensional hyperboloid. These are obtained by the direct solution of differential equations from one-hand side computation of interbasis expansions from the other side. At the calculation of interbasis expansions, we used the asymptotic method designed to solve the problems of quantum mechanics with potential. I discuss also the Inonu-Wigner type contraction from the space of hyperboloids to (pseudo)Euclidean flat space where the radius of the pseudosphere goes to infinity for separable coordinates, wave functions and interbasis expansions.

Speaker Bio: George S. Pogosyan was born in Tbilisi, Georgia (former Soviet Union), in 1952. He obtained both his Ph.D. (1983) and Doctor of Science (2003) from the Joint Institute of Nuclear Research, Dubna (Moscow region), Russia. Pogosyan is a Professor in the Department of Mathematics at the University of Guadalajara, Guadalajara, Mexico, and Director of the Institute for Advanced Studies at Yerevan State University, Yerevan, Armenia. He has more than 120 publications and his research interests include superintegrable systems, contractions of Lie groups and Lie algebras, and symmetry of differential equations.

Presentation Slides: PDF

Contact: H. Cohl

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Last updated: 2016-10-06.