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The pseudospectral method is a powerful tool for finding highly precisesolutions of Schr\"{o}dinger's equation for few-electron problems. We extendthe method's scope to wave functions with non-zero angular momentum and test iton several challenging problems. One group of tests involves the determinationof the nonrelativistic electric dipole oscillator strength for the helium$1^1$S $\to 2^1$P transition. The result achieved, $0.27616499(27)$, iscomparable to the best in the literature.  Another group of test applications is comprised of well-studied leading orderfinite nuclear mass and relativistic corrections for the helium ground state. Astraightforward computation reaches near state-of-the-art accuracy withoutrequiring the implementation of any special-purpose numerics.  All the relevant quantities tested in this paper -- energy eigenvalues,S-state expectation values and bound-bound dipole transitions for S and Pstates -- converge exponentially with increasing resolution and do so atroughly the same rate. Each individual calculation samples and weights theconfiguration space wave function uniquely but all behave in a qualitativelysimilar manner. Quantum mechanical matrix elements are directly and reliablycalculable with pseudospectral methods.  The technical discussion includes a prescription for choosing coordinates andsubdomains to achieve exponential convergence when two-particle Coulombsingularities are present. The prescription does not account for the wavefunction's non-analytic behavior near the three-particle coalescence whichshould eventually hinder the rate of the convergence. Nonetheless the effect issmall in the sense that ignoring the higher-order coalescence does not appearto affect adversely the accuracy of any of the quantities reported nor the rateat which errors diminish.

Pseudospectral Calculation of Helium Wave Functions, Expectation Values, and Oscillator Strength