Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions

It is shown that the spanning set for L2([0, 1]) provided by the eigenfunctions {√2 sin(nπx)}∞ n=1 of the particle in a box in quantum mechanics provides 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 Rd 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 boundN-boson systems.