As stated, the quadratic Stark effect is described by second-order perturbation theory. The zeroth-order eigenproblem
is assumed to be solved. The perturbation theory gives
with the components of the polarizability tensor α defined by
The energy E gives the quadratic Stark effect.
Neglecting the hyperfine structure (which is often justified — unless extremely weak electric fields are considered), the polarizability tensor of atoms is isotropic,
For some molecules this expression is a reasonable approximation, too.
For the ground state  is always positive, i.e., the quadratic Stark shift is always negative.