Hypervirial perturbation theory revisited

A wide range of topics in the area of hypervirial perturbation theory (HVPT ) is discussed. It is shown that with the use of a few simple procedures HV PT is capable of high accuracy for many problems; results from many previou s works in the literature are found to be improvable by the careful use of HVPT with appropriate choice of the unperturbed potential and of the origin at which the energy expansion is carried out. Two multi-well problems from the literature are analysed in detail to show the value of a combination o f HVPT and finite-difference methods.