Wave Propagation in Linear Media | re-examined

8.4 Test of the package
Out[24]= 0
Example 8.4.11 Outside the barrier we must combine the incident and re ected waves to obtain
the desired result. Here the potential vanishes of course.
In[25]:= Schroedinger[0][TriaIncNeg[-t,b,x,d,w,k][xi] +
TriaRefNeg[-t,b,-x,d,w,k][xi]] //Together
Out[25]= 0
Performing these tests on all di erent functions, we see that they satisfy the requirements.
However, with this formal veri cation we can only ensure the correct implementation of the
integrand functions. We cannot check if those parts of the integrals that comprise several
distinct terms (i. e. all transmitted portions of the waves) are put together without error. Nor
can we prove the correctness of the quadrature modules directly. This must be done with
numerical experiments like the ones above. But taking together the results of both formal
and numerical veri cation, we conclude that the implementation is right.
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