  We present application examples of a graphical method for the efficient
construction of potential matrix elements in quantum physics or quantum
chemistry. The simplicity and power of this method are illustrated through
several examples. In particular, a complete set of potential matrix elements
for electron-Lithium scattering are derived for the first time using this
method, which removes the frozen core approximation adopted by previous
studies. This method can be readily adapted to study other many-body quantum
systems.
