  People are familiar with quantum mechanical reflection and transmission
coefficient. In all those cases corresponding potentials are usually assumed as
of constant height and depth. For the cases of varying potential, corresponding
reflection and transmission coefficients can be found out using WKB
approximation method. But due to change of barrier height, reflection and
transmission coefficients should be changed from point to point. Here we show
the analytical expressions of the instantaneous reflection and transmission
coefficients. Here as if we apply the WKB approximation at each point, so we
call it as Instantaneous WKB method or IWKB method. Once we know the forward
and backward wave amplitudes we can find out corresponding wave function by
calculating Eiconal. For the case of analytically complicated potential
corresponding differential equation seems to be unsolvable analytically. If the
potentials are well behaved then obviously these could be replaced by functions
of simple expression of same behaviour which can be integrated analytically and
the equation is now possible to solve analytically.
