Hypervirial analysis of enclosed quantum mechanical systems. I. Dirichlet boundary conditions

Diagonal hypervirial relations are applied to enclosed one-dimensional systems when wave functions obey Dirichlet boundary conditions. A general formula for the energy is derived and it shows a striking difference with the usual formulas through an “extra” term. It constitutes a generalization of previous ones for the virial theorem when there exist nonusual boundary conditions. The values obtained are compared with other approximate methods. Several extensions are proposed.