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A simple method proposed by Harris et al. using the techniques of transformation theory for the generation of the matrix elements of one-dimensional potential functions in a discrete, orthonormal basis is shown to be equivalent to Gaussian quadratures when the basis is constructed of orthogonal polynomials. The basis exp(inθ) on (− π, π) is also discussed.

New upper and lower bounds to the van der Waals C6, C8, and C10 coefficients for hydrogen, noble gas, alkali, and alkaline earth atoms are determined by using Padé approximants to bound the dynamic multipole polarizabilities. Also, the nonadditive, three-body coefficients involving dipole, quadrupole, and octupole interactions are bounded.

The conditions are discussed under which cusps in ϑ trajectories of complex resonance energies correspond to eigenvalues which satisfy the complex virial theorem. (AIP)

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