Penetration into Potential Barriers in Several Dimensions

It is well known that in regions in which the refractive index varies sufficiently slowly, Schrodinger's equation can be very simply treated by using its connexion with Hamilton-Jacobi's differential equation. It is also known that a similar approximation is possible in regions of slowly varying imaginary refractive index (total refiexion). For the latter case the method was developed in papers by Jeffreys (1924), Wentzel (1926), Brillouin (1926) and Kramers (1926). These papers discuss also the behaviour of the wave function in the neighbourhood of the limit between the regions of real and imaginary refractive index…