  The pseudospectral method is a powerful tool for finding highly precise
solutions of Schr\"{o}dinger's equation for few-electron problems. We extend
the method's scope to wave functions with non-zero angular momentum and test it
on several challenging problems. One group of tests involves the determination
of the nonrelativistic electric dipole oscillator strength for the helium
$1^1$S $\to 2^1$P transition. The result achieved, $0.27616499(27)$, is
comparable to the best in the literature.
  Another group of test applications is comprised of well-studied leading order
finite nuclear mass and relativistic corrections for the helium ground state. A
straightforward computation reaches near state-of-the-art accuracy without
requiring 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 P
states -- converge exponentially with increasing resolution and do so at
roughly the same rate. Each individual calculation samples and weights the
configuration space wave function uniquely but all behave in a qualitatively
similar manner. Quantum mechanical matrix elements are directly and reliably
calculable with pseudospectral methods.
  The technical discussion includes a prescription for choosing coordinates and
subdomains to achieve exponential convergence when two-particle Coulomb
singularities are present. The prescription does not account for the wave
function's non-analytic behavior near the three-particle coalescence which
should eventually hinder the rate of the convergence. Nonetheless the effect is
small in the sense that ignoring the higher-order coalescence does not appear
to affect adversely the accuracy of any of the quantities reported nor the rate
at which errors diminish.
