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

Abstract EN

It is shown that the spanning set for L2([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], 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 bound N-boson systems.