In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M\setminus \{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N\setminus \{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.

在本文中，我们表明，对于 3 维流形M上的亚拉普拉斯算子 Δ ，没有以点为中心的点相互作用$q_0\in 米$存在。当M 相对于相关的亚黎曼结构是完整的时，这意味着 Δ 作用于$C_0^{\infty }(米\setminus \{q_0\})$ 本质上是自伴的 ${升}^2(米)$. 一个特殊的例子是海森堡群上的标准亚拉普拉斯算子。这与黎曼流形N 中发生的情况形成鲜明对比，后者的关联拉普拉斯-贝尔特拉米算子作用于$C_0^{\infty }(N\setminus \{q_0\})$ 在本质上从不自伴 ${升}^2(N)$， 如果 $\mathrm{暗淡}N\le 3$. 然后我们将这个结果应用于细分子的薛定谔演化，即惯性矩消失，绕其质心旋转。