Quantum mechanics and the Schrodinger equation are the basis for the de scription of the
properties of atoms molecules and nuclei. The development of reliable meaningful solutions
for the energy eigenfunctions of these many is a formidable problem. The usual approach for
obtaining particle systems the eigenfunctions is based on their variational extremum property
of the expectation values of the energy. However the complexity of these variational solutions
does not allow a transparent compact description of the physical structure. There are some
properties of the wave functions in some specific spatial domains which depend on the general
structure of the Schrodinger equation and the electromagnetic potential. These properties
provide very useful guidelines in developing simple and accurate solutions for the wave
functions of these systems and provide significant insight into their physical structure. This
point though of considerable importance has not received adequate attention. Here we present
a description of the local properties of the wave functions of a collection of particles in
particular the asymptotic properties when one of the particles is far away from the others. The
asymptotic behaviour of this wave function depends primarily on the separation energy of the
outmost particle. The universal significance of the asymptotic behaviour of the wave functions
should be appreciated at both research and pedagogic levels. This is the main aim of our
presentation here.
