Quantum Interference Due to Interaction with a Potential?

Interference is very important in quantum mechanics, but it is apparently difficult to trace its physical origins. In early years of the subject, it appeared there were physical waves present interfering like classical waves, but no such waves were found experimentally. When writing a wavefunction W(x) as a Fourier series, the various sin(px) (for a give symmetry) interfere, i.e. add or subtract depending on the point x. The form of the sin(px) wave already exists for a quantum particle in a box with no potential. In addition, the term -del2 W(x), which is found in the Schrodinger equation and in expressions for kinetic energy density, involves interference of various sin(px) terms in calculating kinetic energy. This is peculiar because a particle in a box has one kinetic energy p*p/2m everywhere even though its wavefunction is sin(px). It seems it would be good to attempt to determine the origins of interference if possible. In this note, it is suggested interference is due to the interaction of a particle with a potential V(x). It is argued that W(x), the wavefunction, is a kind of average of a cycling scattering process with V(x). W(x) contains dynamic information that density W(x)W(x) does not, but is nevertheless a somewhat static looking average as well. It is argued that a quantum particle is continually scattering in the potential in such a manner that a resonance occurs. Thus, sin(px) terms in W(x) are ¨created¨ through this scattering, described by the term V(x)W(x) in the Schrodinger equation. Given that a quantum particle may have zitterbewegung, i.e. forward and backward motion as it moves along with an average v, it seems that this zitterbewegung internal motion affects the scattering with V(x) and may be the origin of interference. The interference which occurs when using average expressions such as the wavefunction W(x), it is argued, is a consequence of this