A simple model potential is used to describe the interaction of a valence electron with the alkali core, which has the correct asymptotic form with the Coulomb and dipolar polarizability terms, and an effective hard-core radius adjusted to give the correct energy for the valence electron. Based on this potential, some simple wave functions are developed to describe the (Na, K, Rb, Cs)-H molecules, which incorporate some important local properties, in particular the cusp property when two charged particles are close to each other. These wave functions provide reliable values for the potential, and a simple physical perspective of their structure. (C) 2003 American Institute of Physics.