Possible Relation Between Quantum Mechanical Cycling exp(iEt) and the Correspondence Principle and Physical Oscillating Objects Like Phonons and PHotons

A value of the average momentum at a point in space may not give information about the times at which each momentum used in the calculation occurred at the point. For example, one could calculate the average at a specific time t or each momentum pi might be associated with a different time ti. For a quantum mechanical particle in a potential, the potential may stirr up different plane waves at different times in a cycling motion dictated by exp(iEt). The higher E, the faster the frequency and the smaller the time interval during which cycling occurs. This cycling involves the quantum system shifting from one momentum to another to create an average momentum at each point in space. If this time is small, then one may imagine an average kinetic energy at a point x at t1 (with a very small time error) and a different average kinetic energy at t2 (also with a very small time error). This averaging process would then resemble a moving classical particle, in addition to following classical probability flow similar to fluid flow. In addition, the cycling of the momentum appears to be a physical phenomenon and seems to indicate a kind periodic interaction with the potential which may be associated with periodic objects such as phonons and photons