Tunnelling through axially summetrical potential barrier

A method is suggested to calculate the sub-barrier wave function for three-dimensional axially symmetrical problems. In the quasiclassical approximation the Schroedinger equation in the vicinity of the most probable tunnelling way is substituted by the parabolic equation which allows the separation of variables for arbitrary potentials. The results are applied to calculate the splitting of energy levels in a double potential well and the broadening of the well in the external field. The results are generalized to the nonstationary case as well