  We further study the validity of the Monte Carlo Hamiltonian method. The
advantage of the method, in comparison with the standard Monte Carlo Lagrangian
approach, is its capability to study the excited states. We consider two
quantum mechanical models: a symmetric one $V(x) = |x|/2$; and an asymmetric
one $V(x)=\infty$, for $x < 0$ and $V(x)=x$, for $x \ge 0$. The results for the
spectrum, wave functions and thermodynamical observables are in agreement with
the analytical or Runge-Kutta calculations.
