Site symmetrized expressions of the atomic temperature factor for all crystallographic point groups have been derived within the framework of the effective one-particle potential formalism. The formulation makes use of the harmonic oscillator eigenfunctions leading to Fourier invariant expressions for the probability density function. The present formalism lends itself for a straightforward application to any crystal structure. The treatment is applied to the analysis of recent neutron diffraction data on zinc. The results are found to be in full accord with those obtained by the use of earlier formalisms.