Semi-classical approximation for tunneling near the top of a potential barrier and its application to solid state physics

We consider the one-dimensional Schrodinger equation with a double-well potential which depends on a small parameter ;In the second part we study the problem of the intraband magnetic breakdown in solid state physics. We show that under certain symmetry conditions this problem can be reduced to the one-dimensional Schrodinger equation considered in the first part of the thesis. We use this to construct approximate solutions for this problem.