The power-law and the logarithmic potentials
  In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The results are in very good agreement with exact numerical results. 
Hakan Ciftci, Engin Ateser and Hueyin Koru