Adiabatic perturbation of a periodic potential. II.(Russian. English summary)Zbl 0643.34068

[For part I see ibid. 58, No.2, 233-243 (1984; Zbl 0534.34064).]
For the equation $$-\psi ''+p(x)\psi +q(\epsilon x)\psi =0$$, p-periodic function, $$\epsilon\to 0$$, behaviour of solutions in neighbourhood of two close turning points is studied. The results give mathematically consistent description of the electric breakdown effect in the Bloch electron theory.

MSC:

 3.4e+21 Singular perturbations, turning point theory, WKB methods for ordinary differential equations

Zbl 0534.34064