The Notion Of Wave Packet Through Systemic Functional Linguistics [1]

Gribbin (1989: 233):

To express itself in particle terms — as a photon, or as an electron — a wave must be confined in some way.  Mathematicians know all about this.  The way to confine a wave is to reduce its purity.  Instead of a single wave with one unique, well-defined frequency, think of a bundle of waves, with a range of frequencies, all moving together.  In some places, the peaks of one wave will combine with the peaks of other waves to produce a strong wave; in other places, the peaks of one wave will coincide with the troughs of other waves, and they will cancel each other out.  Using a technique called Fourier analysis, mathematicians can describe combinations of waves that cancel out almost completely everywhere except within some small, well-defined region of space.  Such combinations are called wave packets.  In principle, as long as you include enough different waves in the packet, you can make it as small as you like. … By losing the purity of a single wave with a unique frequency, we can localise the wave packet until it has the dimensions of an electron.

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From the perspective of Systemic Functional Linguistic theory, the relation between particle and wave is not one of expression (token to value), but one of instantiation (token to type).  A particle, a photon or electron, is each an instance of a (different) type of potential.

Because quantum waves are quantifications of potential in terms of probability, the Fourier analysis is a technique that manipulates the probabilities of quantum potential.  The resultant wave packet is thus a compromise of potential probabilities (wave) and instance frequencies (particle) that arises from not making a clear distinction between potential and instance.