The d-orbitals of a hydrogenic atom with n = 3, l = 2, and m = ±2 are given by:
\(\rm \psi_{3,2\pm 2}=N.R(r)\sin^2\theta e^{\pm2i\phi}\)
Where, N is the normalization constant and R(r) is the radial part of the wavefunction. An appropriate linear combination of these two wavefunctions yields the real orbital
1
dz2
2
dxy
3
dyz
4
dzx