I have encountered the following functional analysis question, which I can't figure out how to prove: Prove that if $H:= - \bar{ \Delta } +V $ on $ L^2 (\mathbb{R}^n) $ , and $lim_{|x| \to \infty} V(x) = + \infty $ , then $H$ has compact resolvent.
Can someone help me figure out how to prove this exercise?
Thanks
( $H:= - \bar{ \Delta } $ stands for the closure of the laplacian)