Define  the d orbital

    Here are two equivalent definitions of the dorbital.  First we use MATHMATICA's Spherical Harmonic[l, m, theta, phi] functions, which are normalized.

Second we consider the actual dependence on the angles.  

Is this function normalized?

    The square of the absolute value of the orbital is proportional to the probability of finding the electron in the orientation defined by Theta, θ, and Phi, φ.  But the orbital give us the preferred orientation of the electronic charge.

    Using ParametricPlot3D, plot a 3-d view of the 3dorbital