We study the n-dimensional Schr\"odinger equation with singular potential
Vλ​(x)=λ∣x∣−2. Its solution space is studied as a global
representation of SL(2,R)​×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