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
Gaithersburg
Thursday, September 29, 2016 13:00-14:00,
Room 4072
Boulder
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. CohlNote: Visitors from outside NIST must contact
Cathy Graham; (301) 975-3800;
at least 24 hours in advance.
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