In the paper by Pierre and Raphael on "The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schroedinger equation", there is a remark on a quadratic form on $H^1(\mathbb{R})$, $H(\epsilon)=\langle L_+\epsilon_1,\epsilon_1\rangle+\langle L_-\epsilon_2,\epsilon_1\rangle$, where $\epsilon_1$, $\epsilon_2$ denote the real an imaginary part of the $H^1$-function $\epsilon$ respectively.
"Note that the quadratic form $H$ is decoupled in the variables $\epsilon_1$, $\epsilon_2$. On each coordinate, a classical elliptic Schrödinger operator with an exponentially decreasing potential underlies the quadratic form. There is then a classical theorem that such a quadratic form has only a finite number of negative directions."
Could somebody give a reference where to find an explaination for that statement?