Wave Propagation in Linear Media | re-examined

A.3 Solutions for the square barrier
PhiGrad[x_, t_, w_, k_, opts___Rule] :=
If[x < 0 || t < 0 || x == 0 && t == 0, 0,
PhiGradEvan[x,t,w,k,opts] + PhiGradTrans[x,t,w,k,opts]];
End[]
SetAttributes[PhiTrans, ReadProtected]
SetAttributes[PhiGradTrans, ReadProtected]
SetAttributes[PhiEvan, ReadProtected]
SetAttributes[PhiGradEvan, ReadProtected]
SetAttributes[PhiRef, ReadProtected]
SetAttributes[PhiInc, ReadProtected]
SetAttributes[Phi, ReadProtected]
SetAttributes[PhiGrad, ReadProtected]
(*
Protect[PhiTrans, PhiGradTrans, PhiEvan, PhiGradEvan]
Protect[PhiRef, PhiInc, Phi, PhiGrad]
*)
EndPackage[]
A.3 Solutions for the square barrier
The package Gauss was written to compute the solutions of the Schrodinger equation for the
tunnelling of an electron through a square barrier (section 4.6). The initial shape of the wave
packet is Gaussian. The details of the implementation are not treated in previous chapters,
however the structure is identical to that of Tunnel.
(* Copyright: Copyright 1997, Institute of Computertechnology, *)
(* Vienna University of Technology *)
(*:Version: Mathematica 2.2.3 *)
(*:Title: Gauss *)
(*:Author: Thilo Sauter *)
(*:Keywords: Tunnel Effect *)
(*:Requirements: None. *)
(*:Warnings: None so far *)
(*:Packages: OscInt *)
(*:Summary: This package computes the solutions of the time-dependent
Schroedinger equation for an initially Gaussian wave packet
tunnelling through a square barrier. It is based on the same
structure as the package Tunnel. The wave integrals are
computed by truncation of the infinite integration range.
*)
(*:History: 31-10-1997 written
*)
BeginPackage["Gauss`", "OscInt`"]
Phi::usage =
"Phi[x,t,w,k,n,l,(opts)] returns the wave function of an initially Gaussian
wave packet at a given coordinate in space and time. The square barrier is
supposed to span the interval x=0 to x=l. Depending on the spatial
coordinate the function either returns the sum of incident and reflected wave,
the portion of the wave inside the tunnel, or the transmitted wave. The parameter
w is the ratio of the carrier frequency of the incident wave and the
characteristic frequency of the barrier. For tunnelling, 0