Further application of an improved systematic variational method for approximating energy levels

A systematic scheme for improving the variational wave functions and corresponding energy levels for two simple one-particle systems is presented. A family of independent wave functions are generated in a systematic fashion about a variational parameter value. The eigenstates are then obtained by diagonalizing the Hamiltonian matrix within the basis and optimized with respect to the variational parameter. This method has been applied to two quantum systems: the quartic anharmonic oscillator and an electron in a uniform electric field. The results for the ground state energies show a convergence comparable to or faster than the conventional Lanczos method. Results are also compared with those from other variational methods. {[}S1050-2947(99)04708-3].