Eigenfunktionen des Drehimpulsoperators
und
in
der Quantenmechanik 4.4
fn(x) = Pn(x) mit 0 ![]() ![]() ![]() ![]() |
(4.26) |
P0(x) = 1 P1(x) = x P2(x) = ![]() ![]() |
(4.27) |
allgemein:
Pn(x) = ![]() ![]() |
(4.28) |
P2n + 1(0) = 0 P2n(0) = (- 1)n![]() ![]() ![]() |
(4.29) |
Rekursionsformel:
(n + 1)Pn + 1(x) = (2n + 1)xPn(x) - nPn - 1(x) | (4.30) |
((1 - x2)![]() ![]() |
(4.31) |
(1 - x2)Pn'(x) = n(Pn - 1(x) - xPn(x)) = ![]() |
(4.32) |
Pl(cos(![]() ![]() ![]() ![]() ![]() ![]() |
(4.33) |
![]() ![]() ![]() ![]() ![]() |
(4.34) |