  In the first part of the paper we consider the Schr\"odinger operator $
-\Delta-V(x),\quad V>0. $ We discuss the relation between the behavior of $V$
at the infinity and the properties of the negative spectrum of $H$. After that,
we consider the case when $V$ changes its sign: $ V=V_+-V_-$, $2V_\pm=|V|\pm V.
$ In this case, we treat $V$ and $-V$ symmetrically and study the relation
between the behavior of $V$ at the infinity and the negative spectra of the
operators $H_+=-\Delta+V$ and $H_-=-\Delta-V$.
