The adiabatic complex WKB method:

Consider the family of equations

where the potentials and  are taken as above.
Assume, moreover that

 is -periodic, not constant and analytic in
 the positive number  is chosen so that 

The parameter  is chosen small (adiabatic).

Change variables  and so that (6) becomes

The consistency condition (2) becomes

and (3), the definition of the monodromy matrix, becomes