1. The problem statement, all variables and given/known data It's not homework. It's just a simple question occured when I'm reading Monte Carlo method in QFT by Colin Morningstar. Of course, I didn't study the QFT earlier. I'm just a regular(or retarded) undergraduate student and I just wanted to learn MCMC technique, and hoped to learn some applications of MCMC in physics. I thought I got the basic idea and already programmed the first example of SHO. However, I noticed he didn't provide proper motivation for MCMC method in order to evaluate vacuum expectation. He provided exact solution of SHO deduced from the path-integral by hand. So, I am wondering now. Why do we have to use MCMC to calculate the VEV, if we are able to calculate exact integral? 2. Relevant equations 3. The attempt at a solution I thought about path integral from what kind of action cannot be calculated. It rules out actions from constant potential, harmonic potential, and Coulomb potential. It's my first posting in this site. If I am violating some kind of rules of this site, please let me know.