Implications of Steady Stream Probabilities on Quantum Mechanics

    Steady state scenarios exist in classical physics and even though there is motion (flows) (i.e. changes in time) overall the system does not change in time. Such systems are usually not described in terms of probability. Furthermore, a single particle moving in one direction is described by x(t), i.e. x=vt, so there is no probability and no steady stream scenario.Such a particle, however, may give rise to a steady stream scenario if it encounters a V1-V2 discontinuity (V1, V2 are two constant potentials) and E (energy) remains constant. In such a case, there is a probability to reflect or to pass into the V2 region with a different p, but the same E. This situation automatically introduces probability and may be associated with a steady stream picture, even in classical physics. As a result, classical physics is not as deterministic as it may seem. If probabilities arise at the discontinuity, one may ask: Is there a steady-stream (flux) type of probability associated with a moving particle? In a steady stream situation there is no change in time, but a moving particle clearly changes in time x(t). How does one associate probabilities which do not contain time to flow problems which clearly contain motion? We investigate these questions and try to argue that the quantum exp(ipx) form and the Born W*(x)W(x) wavefunction picture are associated with these questions.