This is an Oxford MPhys  project undertaken by J J Dudek. 
`Variationally improved perturbation theory' (see S K You et al, Eur. J. Phys. 
19 (1998) 179-186) is applied to the potential -a/r + br, which is relevant 
to heavy quark-antiquark systems. The problem provides an instructive 
`laboratory' for undergraduate exploration, and there are further possibilities 
to be pursued.  The results are published in I. J. R. Aitchison and J.J. Dudek, 
Eur. J. Phys. 23 (2002) 605-614.