here - Faculty of Science - University of Waterloo

Wide-Angle Approximations
• Taylor Series Expansion
1 1 2 1 3 5 4
1+
H ≈ 1+
H − H + H − H + O(
H
2 8 16 128
• Padé [2,0] approximant:
1+
H
≈ 1+
H
2
H
−
8
• Padé [1,1] approximant
1+
H
1+
3H
/ 4
≈
1+
H / 4
1
= 1+
H −
2
2
1
8
H
2
+
1
32
H
3
−
1
128
H
4
5
)
+ O(
H
5
)
Faculty of Science - Department of
Physics 5/3/2009
D. Yevick - Evolution Operators and
Boundary Conditions
9