Elementary Particles: Wave-Like Nature vs Travelling in Wave

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When we say that elementary particles are wave-like in nature does that encompass, lead to and necessarily imply the fact that they travel in wave-like trajectories or is wave-like displacement a separate, distinct notion from their wave-like intrinsic natures?

IH
 
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The trajectory is not sinusoidal, trajectories can just be straight lines. What the wave refers to is the phase of the wave function. I like Feynmann's explanation in his little book QED where the particles carry a clock dial (that indicates their phase). The relative position of the dial then governs what happens when particles meet: constructive or destructive interference.

It may be more educational to indicate phase with color than with wiggly lines.
 
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When we say that elementary particles are wave-like in nature does that encompass, lead to and necessarily imply the fact that they travel in wave-like trajectories or is wave-like displacement a separate, distinct notion from their wave-like intrinsic natures?
Well particles are not wave-like except is some special circumstances ie when in an eigenstate of momentum. What they really are is quantum fields.

This wave-particle duality idea is a left over from the early days of QM and was overthrown when Dirac came up with his transformation theory late in 1926 or when Von Neumann published his classic textbook on it. The choice depends on your attitude to mathematical rigour:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

Thanks
Bill
 

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