Angular functions: Difference between revisions
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| 3 || 3 || fx(x2-3y2) || <math>\frac{1}{4}\sqrt{\frac{35}{2\pi}}\frac{(x^2-3y^2)x}{r^3}</math> | | 3 || 3 || fx(x2-3y2) || <math>\frac{1}{4}\sqrt{\frac{35}{2\pi}}\frac{(x^2-3y^2)x}{r^3}</math> | ||
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:{| border="1" cellspacing="0" cellpadding="5" | |||
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|+ hybrid angular functions | |||
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| sp || sp-1 || <math>\frac{1}{\sqrt 2}\rm s+\frac{1}{\sqrt 2}\rm px</math> | |||
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| || sp-2 || <math>\frac{1}{\sqrt 2}\rm s-\frac{1}{\sqrt 2}\rm px</math> | |||
|- | |||
| sp2 || sp2-1 || <math>\frac{1}{\sqrt 3}\rm s-\frac{1}{\sqrt 6}\rm px+\frac{1}{\sqrt 2}\rm py</math> | |||
|- | |||
| || sp2-2 || <math>\frac{1}{\sqrt 3}\rm s-\frac{1}{\sqrt 6}\rm px-\frac{1}{\sqrt 2}\rm py</math> | |||
|- | |||
| || sp2-2 || <math>\frac{1}{\sqrt 3}\rm s+\frac{2}{\sqrt 6}\rm px</math> | |||
|} | |} | ||
Revision as of 15:30, 13 January 2017
real spherical harmonics l m Name Ylm 0 1 s [math]\displaystyle{ \frac{1}{\sqrt{4\pi}} }[/math] 1 -1 py [math]\displaystyle{ \sqrt{\frac{3}{4\pi}}\frac{y}{r} }[/math] 1 0 pz [math]\displaystyle{ \sqrt{\frac{3}{4\pi}}\frac{z}{r} }[/math] 1 1 py [math]\displaystyle{ \sqrt{\frac{3}{4\pi}}\frac{x}{r} }[/math] 2 -2 dxy [math]\displaystyle{ \frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{xy}{r^2} }[/math] 2 -1 dyz [math]\displaystyle{ \frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{yz}{r^2} }[/math] 2 0 dz2 [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{5}{\pi}}\frac{3z^2-r^2}{r^2} }[/math] 2 1 dxz [math]\displaystyle{ \frac{1}{2}\sqrt{\frac{15}{\pi}}\frac{zx}{r^2} }[/math] 2 2 dx2-y2 [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{15}{\pi}}\frac{x^2-y^2}{r^2} }[/math] 3 -3 fy(3x2-y2) [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{35}{2\pi}}\frac{(3x^2-y^2)y}{r^3} }[/math] 3 -2 fxyz [math]\displaystyle{ \frac{1}{2}\sqrt{\frac{105}{\pi}}\frac{xyz}{r^3} }[/math] 3 -1 fyz2 [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{21}{2\pi}}\frac{(5z^2-r^2)y}{r^3} }[/math] 3 0 fz3 [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{7}{\pi}}\frac{(5z^2-3r^2)z}{r^3} }[/math] 3 1 fxz2 [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{21}{2\pi}}\frac{(5z^2-r^2)x}{r^3} }[/math] 3 2 fz(x2-y2) [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{105}{\pi}}\frac{(x^2-y^2)z}{r^3} }[/math] 3 3 fx(x2-3y2) [math]\displaystyle{ \frac{1}{4}\sqrt{\frac{35}{2\pi}}\frac{(x^2-3y^2)x}{r^3} }[/math]
hybrid angular functions sp sp-1 [math]\displaystyle{ \frac{1}{\sqrt 2}\rm s+\frac{1}{\sqrt 2}\rm px }[/math] sp-2 [math]\displaystyle{ \frac{1}{\sqrt 2}\rm s-\frac{1}{\sqrt 2}\rm px }[/math] sp2 sp2-1 [math]\displaystyle{ \frac{1}{\sqrt 3}\rm s-\frac{1}{\sqrt 6}\rm px+\frac{1}{\sqrt 2}\rm py }[/math] sp2-2 [math]\displaystyle{ \frac{1}{\sqrt 3}\rm s-\frac{1}{\sqrt 6}\rm px-\frac{1}{\sqrt 2}\rm py }[/math] sp2-2 [math]\displaystyle{ \frac{1}{\sqrt 3}\rm s+\frac{2}{\sqrt 6}\rm px }[/math]