Real space methods and in particular the wavelet based method have convincing fundamental advantages as basis sets for electronic structure calculations. Nevertheless they are not widely used. One reason for this are large prefactors in various operations. We perform a mathematical convergence and performance analysis of various implementations of wavelet algorithms that have been proposed in an ad hoc manner in the physics literature for the solution of Schrödinger's equation. There is at present no method that would allow to calculate the potential energy in an efficient way if the Daubechies wavelets are used. However for the interpolating wavelets there is a fast and accurate scheme that is expected to make wavelets more efficient for electronic structure calculations than the best finite difference schemes.