Wave Functions in Momentum Space

Abstract

The integral equation, satisfied by the momentum-space wave function $\phi \mathrm{}\left(p\right)\mathrm{}$ for a nonrelativistic two-body problem with a phenomenological central interaction potential, is solved by means of an iteration method. A general prescription is given for finding suitable trial wave functions, which depend on some adjustable parameters. Reasonable values for these parameters are found by iteration of the wave function for particularly convenient values of the momentum. Successive iterations, giving better approximations ${\phi }_n\mathrm{}\left(p\right)\mathrm{}$ for $\phi \mathrm{}\left(p\right)\mathrm{}$, are carried out in a form suitable for numerical work. Besides ${\phi }_n\mathrm{}\left(p\right)\mathrm{}$, approximations are obtained for (a) the binding energy for certain bound states and (b) the phase shifts for scattering problems. For scattering at fairly low energies reasonable approximations are obtained with the same method both for weak and for fairly strong potentials.