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There are two parts: If the wavepacket is a superposition of plane waves, in what sense are they "quantum states wherein the particle is exactly localized"?

And if this was so, why in the bound state wavepacket case this can never be so?

- Thread starter TrickyDicky
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- #1

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There are two parts: If the wavepacket is a superposition of plane waves, in what sense are they "quantum states wherein the particle is exactly localized"?

And if this was so, why in the bound state wavepacket case this can never be so?

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kith

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You could writeThere are two parts: If the wavepacket is a superposition of plane waves, in what sense are they "quantum states wherein the particle is exactly localized"?

[tex]e^{-ipx'} \propto \int_{-\infty}^{+\infty} \delta(x-x') e^{-ip(x-x')} dx,[/tex]

so in this sense, a plane wave can be viewed as a formal superposition of delta functions just like a Gaussian wavepacket can be viewed as a formal superposition of plane waves. But as you probably know, delta functions are not square integrable so they are not proper quantum states but idealizations.

This probably refers to entanglement. If the composite state is not a product state, you cannot assign definite wavefunctions to the single particles at all.And if this was so, why in the bound state wavepacket case this can never be so?

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Yes, they are idealizations, with certain validity as approximations for many different situations(like for VP propagators) but not to undermine the very foundation of QM, the HUP. It looks like in particle physics they take seriously this idealization, the paragraph I quoted goes on to say: "It is in this sense that physicists can discuss the intrinsic "size" of a particle: The size of its internal structure, not the size of its wavepacket. The "size" of an elementary particle, in this sense, is exactly zero."You could write

[tex]e^{-ipx'} \propto \int_{-\infty}^{+\infty} \delta(x-x') e^{-ip(x-x')} dx,[/tex]

so in this sense, a plane wave can be viewed as a formal superposition of delta functions just like a Gaussian wavepacket can be viewed as a formal superposition of plane waves. But as you probably know, delta functions are not square integrable so they are not proper quantum states but idealizations.

Since in particle physics this assumption about the internal structure of elementary particles is essential to their interpretation of scattering experiments of i.e.electrons as probes of the internal structure of i.e. protons I wonder if some inconsistency can be derived from this de facto dispensing with the HUP.

I see what you mean, you cannot assign them states since when considering the isolated composite particle they are acting as virtual, so this is by definition. What I find ironic here is that the composite state itself is mathematically equivalent to elementary particle one, even if physically by definition we cannot assign it the same meaning as in the elementary particle case.This probably refers to entanglement. If the composite state is not a product state, you cannot assign definite wavefunctions to the single particles at all.

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