Path Integral Monte Carlo Solution of the Harmonic Potential

In the notebook, we discuss and solve the following propagator:

$$k(x_bt_b|x_at_a) = \int_{x_a}^{x_b}D[x(t)] \exp\left(i\int_{t_a}^{t_b}dt\frac{m}{2}\left[\dot{x}^2 - x^2\right]\right),$$

where we take $$\hbar = \omega = 1$$. More information can be found in the notebook.