The Real Spherical Harmonics

Definition: \[ m=0: \qquad Y_{l0}= \sqrt{\frac{2l+1}{4\pi}} \quad P_l^{0} (cos(\theta)) \] \[ m>0: \qquad Y_{lm}= (-1)^m \sqrt{2} \sqrt{\frac{2l+1}{4\pi} \frac{(l-m)!}{(l+m)!}} \quad P_l^{m} (cos(\theta)) \quad cos(m \varphi) \]

• Choose a representation of the functions from the menu:
  • Colored Surface: using a sphere and color it w.r.t value of the function
  • Magnitude Mapped: using the magnitude as radii and shape a structure (also colored like the sphere)
  
  
• Then you can choose l and m.
• The coloring is conected with the value of the function at this position:
  • red = negativ maximum;
  • yellow = Zero;
  • green = positiv maximum