Eigenvalue lower bounds with Bazley’s special choice of an infinite-dimensional subspace

摘要

Bazley’s special choice of a finite-dimensional space to construct an intermediate operator between a base operator and the full Hamiltonian is a standard technique to calculate lower bounds to the energies of a system. We modify Bazley’s method to accommodate an infinite-dimensional space that is complete in one particle of the system. An application to the helium atom shows improvement in the lower bound to the ground-state energy, indicating promise in our method. However, significant problems are revealed which include (1) poorer bounds for the excited states, (2) lack of symmetry in the intermediate operator, and (3) lack of direction for improvement.