Several methods for obtaining the positron wavefunction in the two-photon annihilation studies have been outlined. Numerical methods of integrating the Schrodinger equation and the Dirac equation with relevant boundary conditions have been discussed and the wavefunctions so obtained are compared with the one computed by extending the APW formalism to positrons. It is shown that there is no need to resort to relativistic methods to compute the positron wavefunction in solids of high atomic number although the electrons are to be treated relativistically.