Repeat the previous problem but use only the four properties of the Poisson bracket and the particular Poisson brackets between the components of the position and momentum vectors. From this, deduce the corresponding commutation relations in quantum mechanics.

Data from previous problem

Compute the Poisson bracket of any components of position or momentum with any component of angular momentum. Use the Poisson bracket representation as derivatives with respect to canonical coordinates and momenta. You might find it useful to write \(L^{i}=\varepsilon^{i j k} x^{j} p^{k}\), and use identities involving the totally antisymmetric tensor \(\varepsilon^{i j k}\).