10. Appendix

670 Appendix B
to the waves A1 and B1 via a product of transfer matrices M1, M2, ..., Mn1:
A1
An1
M1M2...Mn
B1
Bn1
Each transfer matrix Mi isa2× 2 matrix of the form:
Mi
Mi(1, 1)
Mi(1, 2)
Mi(2, 1) Mi(2, 2)
whose elements are given in Eqs. (9.59a) to (9.59d):
M1(1, 1)
M1(1, 2)
M1(2, 1)
M1(2, 2)
1 m1k2
exp i(k2 k1) d2
2 2m2k1
d1
2
1 m1k2
exp i(k2 k1) d2
2 2m2k1
d1
2
1 m1k2
exp i(k2 k1) d2
2 2m2k1
d1
2
1 m1k2
exp i(k2 k1) d2
2 2m2k1
d1
2
(9.14c)
(9.14d)
(9.14e)
(9.14f)
(9.14g)
(9.14h)
The transfer matrices M2, M3, and M4 can be obtained similarly. The product
(Mij) of the four matrices M1, ..., M4 can be calculated with a computer
program, such as Mathematica, Mathcad etc. T(0) can obtained by assuming
that there will be no reflected wave in region 5 so B5 0 and A1 M11A5:
T(0) |A5/A1| 2 |1/M11| 2 .
The following plot of T(0) vs E has been obtained by using the program
Mathcad. The program codes are shown in a separate file labeled
as Problem9.14 Codes.mcd which can be downloaded from the website:
http://pauline.berkeley.edu/book/SolutionsNew.html.