Multiple internal reflections method in the description of tunneling evolution of nonrelativistic particles and photons

The non-stationary solution method for a problem of tunneling of nonrelativistic particles and photons through a barrier on the basis of multiple internal reflections of wave packets in relation of barrier boundaries is submitted. The method is described and proved in solving an one-dimensional problem of tunneling of the particle through a rectangular barrier. For problems of tunneling of the particle through a spherically symmetric barrier and the photon through an one-dimensional barrier the amplitudes of transmitted and reflected wave packets in relation to the barrier, times of the tunneling and the reflection are found using of the method. Hartman's and Fletcher's effect is analysed