Enclosed quantum systems: use of the direct variational method

A variational boundary perturbation method for solving Schrodinger's equation for enclosed quantum systems with infinite potential walls has been recently proposed by Gorecki and Byers Brown. Their treatment was based on the use of an input wavefunction chi =Gc0 f, where chi 0 is the wavefunction of the free system and f a non-singular function that vanishes at the boundary. The class of functions f was further used to minimize the total energy. In the present work the direct variational method is applied to the ansatz function chi by assigning the variational parameter to the free-system wavefunction, once an adequate cut-off function, f, is defined. This is in contrast to the previous authors' work. The procedure is applied to hydrogen and helium atoms within hard spherical boxes and also to a hydrogen atom confined between two impenetrable parallel walls. The results are in fair agreement with exact calculations.