here - Faculty of Science - University of Waterloo

Transition, Propagation Operator
+
Ψin
j
−
Ψin
j
+
Ψout
j + 1
−
Ψout
j + 1
P
m
=
⎛e
⎜
⎝0
− jk
o
n
om
L
e
m
jk
z
o
n
om
L
0
m
z
⎟ ⎞
⎠
T
j
=
⎛
⎜1+
1 ⎜
⎜
2 ⎜
⎜1−
⎝
n
n
n
o
n
o
o
j+
1
o
j
j
j+
1
L
L
−1
j+
1
−1
j+
1
L
L
j
j
1−
1+
n
n
n
o
n
o
o
j+
1
o
j
j
j+
1
L
L
−1
j+
1
−1
j+
1
L
L
j
j
⎞
⎟
⎟
⎟
⎟
⎟
⎠
Faculty of Science - Department of
Physics 5/3/2009
D. Yevick - Evolution Operators and
Boundary Conditions
47