Abstract:
A differential equation of the form
[−d2dx2+p(x)+q(εx)]f=0 is
considered. The coefficient p is assumed to be a periodic
function: p(x+a)=p(x). The behavior of the solutions for
|ε|≪1 is studied. The concept of a turning point is
generalized to this case, and self-consistent asymptotic
expressions are obtained for the solutions at a certain distance
from the turning points and in their neighborhoods. For p=0, the
obtained expressions agree with the classical WKB expressions.
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