Quantum States by Iterative Discrete Spectral Analysis.

Wave function independence is shown to be attainable in quantum state calculations through the synthesis of a direct iterative eigenvalue technique with the discrete spectral method of solution. The Hamiltonian operator reduces to a bounded phase space function if the kinetic term is defined on a uniformly discretized momentum space with the potential defined on the conjugate configuration space. Consideration of this discretized phase space function as a representation of the Hamiltonian matrix allows energy levels to be evaluated through iteration with an initial arbitrary vector which may be orthogonalized at convergence to yield an initial arbitrary excited state vector. A further synthesis of this method with spline functions, which are used to model wave function dependent potentials, allows its extension to self-consistent calculations. This self-consistent iterative pseudospectral method is then used to evaluate the configuration energy of an excess anionic charge present in a polar fluid which may be bounded by a conducting medium. Using a continuum model for the solvent it is found that the election affinity of an isolated ammoniated oxygen atom is 0.290 Ry +/- 0.001 Ry (3.94 eV) increasing to 0.350 Ry (4.76 eV) at a nuclear distance of 4a_0 from a metal surface.