Consider a linear operator $H\colon L^2(\mathbb{R}^3)\to L^2(\mathbb{R}^3)$ given by $$H(\psi)(x):=-\Delta\psi(x)+V(x)\cdot \psi(x),$$ where $V\colon \mathbb{R}^3\to \mathbb{R}$ is a continuous (or smooth) non-negative function. If necessary, one may assume $\lim_{|x|\to \infty}V(x)=+\infty$.

Are there known estimates from below of the minimal eigenvalue of $H$ in terms of $V$?

(Of course, the trivial estimate is by 0.)

I am not an expert and may not aware even of the most standard results.