Probability of tunneling through potential barriers in more than one dimension

Probabilities of tunneling through two-dimensional and axially symmetrical potential barriers are calculated for the wave falling on a caustic by the angle near $90^\circ$. The results are applied to the calculation of the broadening of energy levels in a potential well in an external field and the splitting in a double potential well. In the case of motion with small angular moments in wells the formulas obtained coincide with those known before. Under the special assumptions the probability of tunneling through a potential barrier of arbitrary dimension is calculated.