  The notion of the optimized perturbation, which has been successfully applied
to energy eigenvalues, is generalized to treat wave functions of quantum
systems. The key ingredient is to construct an envelope of a set of
perturbative wave functions. This leads to a condition similar to that obtained
from the principle of minimal sensitivity. Applications of the method to
quantum anharmonic oscillator and the double well potential show that uniformly
valid wave functions with correct asymptotic behavior are obtained in the
first-order optimized perturbation even for strong couplings.
