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arXiv · 1110.1030

Global representations of the Heat and Schrödinger equation with singular potential

Jose Franco·Mark Sepanski
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Abstract

We study the $n$-dimensional Schrödinger equation with singular potential $V_λ(x)=λ|x|^{-2}$. 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 $λ$ 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.

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Jose Franco, Mark Sepanski. 2013-02-15. Global representations of the Heat and Schrödinger equation with singular potential. https://arxiv.org/abs/1110.1030

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