Jose A. Franco, Mark R. Sepanski
Abstract:
The n-dimensional Schrodinger equation with a singular potential
is studied.
Its solution space is studied as a global representation of
. A special subspace of solutions
for which the action globalizes is constructed via nonstandard
induction outside the semisimple category. The space of K-finite
vectors is calculated, obtaining conditions for
so that this
space is non-empty. The direct sum of solution spaces over such admissible
values of
is studied as a representation of the (2n+1)-dimensional
Heisenberg group.
Submitted February 28, 2013. Published July 2, 2013.
Math Subject Classifications: 22E70, 35Q41.
Key Words: Schr\"{o}dinger equation; heat equation; singular potential;
Lie theory; \hfill\break\indent representation theory; globalization
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Jose A. Franco University of North Florida 1 UNF Drive, Jacksonville, FL 32082, USA email: jose.franco@unf.edu | |
Mark R. Sepanski Baylor University, One Bear Place # 97328 Waco, TX 76798, USA email: mark_sepanski@baylor.edu |
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