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Bound states of the power-law and logarithmic potentials are calculated usinga generalized pseudospectral method. The solution of the single-particleSchr\"odinger equation in a nonuniform and optimal spatial discretizationoffers accurate eigenvalues, densities and expectation values. The calculationsare carried out for states with arbitrary $n$ and $\ell$ quantum numbers.Comparisons are made with the available literature data and excellent agreementis observed. In all the cases, the present method yields considerably improvedresults over the other existing calculations. Some new states are reported.

Calculation of the bound states of power-law and logarithmic potentials through a generalized pseudospectral method