  Following the approach of our previous paper we continue to study the
asymptotic solution of periodic Schr\"{o}dinger operators. Using the
eigenvalues obtained earlier the corresponding asymptotic wave functions are
derived. This gives further evidence in favor of the monodromy relations for
the Floquet exponent proposed in the previous paper. In particular, the large
energy asymptotic wave functions are related to the instanton partition
function of N=2 supersymmetric gauge theory with surface operator. A relevant
number theoretic dessert is appended.
