Angular functions: Difference between revisions

Revision as of 14:51, 13 January 2017

l	m	Name	Y_lm
0	1	s	$\frac{1}{\sqrt{4\pi}}$
1	-1	py	$\sqrt{\frac{3}{4\pi}}\frac{y}{r}$
1	0	pz	$\sqrt{\frac{3}{4\pi}}\frac{z}{r}$
1	1	py	$\sqrt{\frac{3}{4\pi}}\frac{x}{r}$
2	-2	dxy	$\frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{xy}{r^2}$
2	-1	dyz	$\frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{yz}{r^2}$
2	0	dz2	$\frac{1}{4}\sqrt{\frac{5}{\pi}}\frac{3z^2-r^2}{r^2}$
2	1	dxz	$\frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{zx}{r^2}$
2	2	dx2-y2	$\frac{1}{4}\sqrt{\frac{15}{\pi}}\frac{x^2-y^2}{r^2}$

@@ Line 7: / Line 7: @@
 |-
 |  0 ||  1 || s || <math>\frac{1}{\sqrt{4\pi}}</math>
+|-
+|  1 || -1 || py || <math>\sqrt{\frac{3}{4\pi}}\frac{y}{r}</math>
+|-
+|  1 ||  0 || pz || <math>\sqrt{\frac{3}{4\pi}}\frac{z}{r}</math>
+|-
+|  1 ||  1 || py || <math>\sqrt{\frac{3}{4\pi}}\frac{x}{r}</math>
+|-
+|  2 || -2 || dxy    || <math>\frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{xy}{r^2}</math>
+|-
+|  2 || -1 || dyz    || <math>\frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{yz}{r^2}</math>
+|-
+|  2 ||  0 || dz2    || <math>\frac{1}{4}\sqrt{\frac{5}{\pi}}\frac{3z^2-r^2}{r^2}</math>
+|-
+|  2 ||  1 || dxz    || <math>\frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{zx}{r^2}</math>
+|-
+|  2 ||  2 || dx2-y2 || <math>\frac{1}{4}\sqrt{\frac{15}{\pi}}\frac{x^2-y^2}{r^2}</math>
 |}