Global representations of the Heat and Schrödinger equation with singular potential

Details Global representations of the Heat and Schrödinger equation with singular potential Global representations of the Heat and Schrödinger equation with singular potential

2011-10-05

arxiv.org/abs/1110.1030v2

Mathematics

Representation Theory

Scientific paper

We study the $n$-dimensional Schr\"odinger equation with singular potential $V_\lambda(x)=\lambda |x|^{-2}$. Its solution space is studied as a global representation of $\widetilde{SL(2,\R)}\times O(n)$. 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 $\lambda$ so that this space is non-empty. The direct sum of solution spaces, over such admissible values of $\lambda$ is studied as a representation of the $2n+1$-dimensional Heisenberg group.

Affiliated with

Also associated with

No associations

Rating

Global representations of the Heat and Schrödinger equation with singular potential does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global representations of the Heat and Schrödinger equation with singular potential, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global representations of the Heat and Schrödinger equation with singular potential will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325789