Quantum Mechanical Aspects in Classical Physics

In a series of notes we examined a 2x2 matrix model which is naturally incorporated into Einstein´s 1905 energy momentum equation p2 + m2 = E2 (1). We showed that it was possible to obtain energy, velocity and momentum matrices, calculate expectation, dispersion values and establish exp(-iHt) as the time evolution operator. From this, we calculated zitterbewegung and the time dependence of other matrices. The purpose of this note is to see if this formalism, established for a relativistic model can also be applied to the nonrelativistic case. Several cases are considered. Next, we try to apply the model to the case of a classical spring, which is related to the production of phonons.In this case, we apply the mathematics of the model to the classical spring, not the model itself. It is found that one can obtain a velocity matrix and find an energy matrix with time evolution of exp(-iHt). Furthermore, it appears that time dependent operator calculations predict classical periodic motion with a period of sqrt(k/m), where k is the spring constant and m the mass.