Angular Wave Function of three p and five d Orbitals

Angular Wave Function of three p and five d Orbitals

Angular Wave Function of three p and five d Orbitals

Angular Wave Function of three p and five d Orbitals with normalization factors

Angular wave function of three p and five d orbitals with normalization factors are given below-
For p orbital, l = 1
l = 1       m = 0         (2pz)       =     cosθ

l = 1       m = +1       (2px)       =     sinθ.cosφ

l = 1       m = −1       (2py)       =     sinθ.sinφ

For d orbital, l = 2
l = 2       m = 0         (3dz2)       =     3cos2θ − 1

l = 2       m = +1         (dxz)       =     sinθ.cosθ.cosφ

l = 2       m = −1         (dyz)       =     sinθ.cosθ.sinφ

l = 2       m = +2         (dx2−y2)       =     sin2θ.cos2φ

l = 2       m = −2         (dxy)       =     sin2θ.sin2φ