Ebert - Psi-k
Ebert - Psi-k
Ebert - Psi-k
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Ludwig<br />
Maximilians-<br />
Universität<br />
München<br />
Spherical functions j l (kr) and n l (kr)<br />
spherical Bessel functions<br />
j l (kr)<br />
von Neumann functions<br />
n l (kr)<br />
0.4<br />
0.2<br />
l=0<br />
l=1<br />
l=2<br />
0.4<br />
0.2<br />
l=0<br />
l=1<br />
l=2<br />
j l<br />
(kr)<br />
0<br />
n l<br />
(kr)<br />
0<br />
-0.2<br />
-0.2<br />
-0.4<br />
0 5 10 15 20<br />
regular<br />
irregular<br />
kr<br />
(kr) l<br />
(2l+1)!!<br />
asymptotic behavior<br />
0←r<br />
←−<br />
-0.4<br />
0 5 10 15 20<br />
j l (kr)<br />
r→∞<br />
−→<br />
kr<br />
1<br />
kr sin(kr − l π 2 )<br />
− (2l−1)!!<br />
(kr) l+1 n l (kr) − 1<br />
kr cos(kr − l π 2 )<br />
KKR07 – p.22/100
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