  Introducing the notion of extended Schr\"odinger spaces, we define the
criticality and subcriticality of Schr\"odinger forms in the same manner as the
recurrence and transience of Dirichlet forms, and give a sufficient condition
for the subcriticality of Schr\"odinger forms in terms the bottom of spectrum.
We define a subclass of Hardy potentials and prove that Schr\"odinger forms
with potentials in this subclass are always critical, which leads us to optimal
Hardy type inequality. We show that this definition of criticality and
subcriticality is equivalent to that there exists an excessive function with
respect to Schr\"odinger semigroup and its generating Dirichlet form through
$h$-transform is recurrent and transient respectively. As an application, we
can show the recurrence and transience of a family of Dirichlet forms by
showing the criticality and subcriticaly of Schr\"odinger forms and show the
other way around through $h$-transform, We give a such example with fractional
Schr\"odinger operators with Hardy potential.
