Multidimensional integration: partition and conquer

Understanding the behavior of particles subjected to forces is a basic theme in physics. The simplest system is a set of particles confined to motion along a line, but even this type of system presents computational challenges. For the harmonic oscillator, a particle is subjected to a force directed toward the origin and proportional to the distance between the particle and the origin. The resulting potential is V(x) = 1/2 αx² where α is a constant. This system is quite thoroughly understood, and quantities of interest can be computed in closed form. Alternatively, the Ginzburg-Landau anharmonic potential, - 1/2 αx² + 1/4 βx⁴ (α and β are constant), is related to solution of the Schrodinger equation, and quantities of interest are computed approximately. One method of obtaining such approximations is numerical integration, which is our focus in this assignment.