A great variety of numerical methods have been employed to solve the Schroedinger equation, the basic equation of theoretical atomic physics. Being a three body problem, the scattering of an incoming antiproton (p−) by a hydrogen atom (H, consisting of an electron, e−, bound to a proton, p) is one of the simplest problems in field of atomic theory that requires a numerical solution. Described and compared here are three methods, valid in essentially separate energy ranges from zero energy through MeV energies, that illustrate how numerical methods are employed in this field. In spite of this problem's seeming simplicity, much effort is required in terms of mathematical manipulation and use of approximations to render it capable of numerical solution.