Iteration-Variation Procedures for Quantum-Mechanical Perturbations

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Abstract
The Dalgarno—Lewis procedure is used for obtaining explicit solutions to the perturbation equations. Three basic ideas are exploited: (1) By using the wavefunction through the first order as the zeroth‐order wavefunction in a new perturbation calculation, we obtain an iteration procedure that converges with surprising rapidity. After n iterations, the energy is given accurately up to terms of the order of the 2n+1 power of a perturbation parameter. (2) By varying the proportions of the zeroth‐ and first‐order functions in the wavefunction through the first order, we obtain somewhat better energies and still maintain the ability to iterate. (3) For degenerate and almost degenerate energy levels, the wavefunctions through the first order and the energies through the third order are obtained by solving a finite‐ordered secular equation. This procedure is much simpler and less apt to fail than the usual techniques.

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