Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems indDimensions

Abstract

It is shown that the spanning set forL2([0,1])provided by the eigenfunctions{2sin(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], whereaandbare then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box inRdturns out to be appropriate also for problems that are softly confined byU-shaped potentials, including those with strong singularities atr=0. Specific examples are discussed in detail, along with some boundN-boson systems.