Useful Bases for Problems in Nuclear and Particle Physics

Abstract

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space and can be exactly Fourier-Bessel transformed. The configuration space functions are associated Laguerre polynomials multiplied by an exponential weight, and their Fourier-Bessel transforms can be expressed in terms of Jacobi polynomials in $Λ^2/(k^2 + Λ^2)$. A simple model of a meson containing a confined quark-antiquark pair shows that this basis is much better at describing the high-momentum properties of the wave function than the harmonic-oscillator basis.