Interference, Reduced Action, and Trajectories

Abstract

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the trajectories of the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.

Welcher Weg? A Trajectory Representation of a Quantum Young’s Diffraction Experiment

“…A companion article shows how the deterministic trajectory representation exhibits interference effects between plane wave functions that is consistent with the quantum equivalence principle of Faraggi and Matone [4] and does not resort to Born's probability density of the Copenhagen interpretation [3].…”

“…The two point secondary source problem is azimuthally invariant. A dispherical wave function, ψ d can be synthesized from its two components, ψ 1 and ψ 2 , by [3] …”

“…For completeness, the cosine term in the amplitude for ψ d in (3) manifests interference. A generator of the motion, the reduced action (Hamilton's characteristic function), W d , for the self-entangled wave function can be extracted from (3) as [3] W d = arctan r 2 sin(k 1 · r 1 ) + r 1 sin(k 2 · r 2 ) r 2 cos(k 1 · r 1 ) + r 1 cos(k 2 · r 2 )…”

“…The trajectory representation has been developed as a deterministic theory of quantum mechanics [1][2][3][4][5][6][7][8]. Faraggi and Matone have shown that the foundations of quantum mechanics can be developed from the quantum equivalence principle, which is consistent with the trajectory theory, without any of the philosophy of the Copenhagen interpretation [4].…”

Density dynamics in some quantum systems

“…[54][55][56][57][58] The inherent nonlocality of quantum systems gives rise to phenomena such as entanglement. Quantum entanglement is demonstrated in problems such as wave packet spreading [59] and quantum Young's diffraction experiment [60] by means of quantum trajectory-based calculation. Bittner and coworkers have used the supersymmetry algebra in solving multidimensional problems involving rare gas clusters with up to 130 atoms.…”