Consider a simple one-dimensional quantum harmonic oscillator with Lagrangian L = 1 2 mx² - 1/mw²x². Compute the amplitude K(xf, tf; xi, t;) for the particle to travel from x; at time t; to xƒ at time xf in the path integral formalism (the propagator) using the discretization of the path integral. You should rewrite the trajectory as the classical trajectory (the solution of the Euler-Lagrange equations) plus the deviation from it (x(t) = xc1(t) + y(t)). Describe in words the result obtained (a plot is useful)