  It is shown that the spanning set for L^2([0, 1]) provided by the
eigenfunctions {sqrt{2} sin(n\pi x)}_{n=1}^{\infty} of the particle-in-a-box in
quantum mechanics provide a very effective variational basis for more general
problems. The basis is scaled to [a,b], where a and b are then used as
variational parameters. What is perhaps a natural basis for quantum systems
confined to a spherical box in R^d, turns out to be appropriate also for
problems that are softly confined by U-shaped potentials, including those with
strong singularities at r=0. Specific examples are discussed in detail, along
with some bound N-boson systems
