Global representations of the Heat and Schrödinger equation with singular potential

Original · EN

We study the n-dimensional Schrödinger equation with singular potential Vλ(x)=λ|x|⁻². Its solution space is studied as a global representation of SL(2,)× O(n). 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 λ so that this space is non-empty. The direct sum of solution spaces, over such admissible values of λ is studied as a representation of the 2n+1-dimensional Heisenberg group.