Helium Wave Function in Momentum Space

Approximate solutions to the integral Schrödinger equation in momentum space are obtained. The iteration scheme of Svartholm is used to obtain the first iterated wave function and the half-iterated energy. A wave function of the type $\phi =\Sigma C_{\mathrm{ij}}\left[\exp \right(-{\alpha }_i{p_1}^2-{\alpha }_j{p_2}^2)+\exp (-{\alpha }_j{p_1}^2-{\alpha }_i{p_2}^2\left)\right]$ is employed to start the iteration procedure. The best energy value computed using a wave function with three nonlinear parameters is -2.8915 atomic units. This energy is to be compared with the result of a conventional variational calculation using the same wave function in coordinate space, -2.85112 atomic units.