  I describe how simulations of lattice QCD using the path integral formulation
provide the two basic quantum mechanical properties of QCD, its ground state in
which correlation functions are calculated, and Fock state wavefunctions
between which matrix elements of operators are calculated. Both constructs are
stochastic, so unfortunately one gets no intuitive picture or even a
qualitative understanding of what they look like, nevertheless they contain and
display all the subtleties of the quantum field theory. Today, these
simulations provide many quantities that are impacting phenomenology and
experiments. I illustrate the methods and the steps in the analysis using, as
examples, three observables: the isovector charges of the nucleon, the
contribution of the quark's intrinsic spin to the nucleon spin, and the
pion-nucleon sigma term.
