  Stimulated by the category theorems of Eisner and Ser\'eny in the setting of
unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove
category theorems for Schr\"odinger semigroups. Specifically, we show that, to
a given class of Schr\"{o}dinger semigroups, Baire generically the semigroups
are strongly stable but not exponentially stable. We also present a typical
spectral property of the corresponding Schr\"{o}dinger operators.
