New Equation for Lower Bounds to Eigenvalues with Application to the Helium Atom

There is currently considerable interest in lower bound procedures based on the method of intermediate Hamiltonians. The method relies on a theorem which states that if the hermitian operators A and B satisfy the inequality A<B, then their ordered eigenvalues respectively satisfy the same inequality. Thus to find lower bounds to the eigenvalues of a Hamiltonian H, we must find a comparison operator H to the l power, such that H to the l power less than or equal to H, and such that H to the l power is simple enough for its eigenvalue problem to be solved. (Author)