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Whenever we have a "macro" object like a buckyball, it has many electrons and quarks if not something more fundamental, all of which have their own wavefunctions that interact with each other. But in the double-slit experiment, we show that the minimas and maximas occure for only photons/electrons with a single wavelength. If we take a combination of wavelengths, like visible light, we won't have a distinct interference pattern. (although we do see some separation at the edges of bright intensity bands)

Then, how is it possible that something that is a combination of various matter waves with different wavelengths like a buckyball, also shows the same kind of interference pattern?

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    $\begingroup$ This question would benefit from some references to such experiments, because the issues you raise are certainly addressed in the papers describing the experiments for a skeptical audience. $\endgroup$ – rob Nov 18 '19 at 19:51
  • $\begingroup$ It would be too good to be true if the interference pattern for a certain particle depended sensitively on the details of its internal structure. This would be like an infinitely powerful microscope, and we wouldn't need to build particle accelerators. $\endgroup$ – user4552 Nov 18 '19 at 23:43
  • $\begingroup$ @Rob Can I please ask you to add some links to the question that you find are suitable and would benefit a wide audience? I came across this question after reading some articles on how "recently" double slit experiment was tested on macro objects. $\endgroup$ – NiRVANA Nov 20 '19 at 12:19
  • $\begingroup$ @BenCrowell, does it not happen, at least in case of protons? i.e the wavefunctions of quarks being combined to give wavefunction of proton or neutrons? Also, to write the hamiltonian of any system, don't I need to kow the internal workings of it? Which means, basically I shall be including wavefinctions of internal particles, if any. $\endgroup$ – NiRVANA Nov 20 '19 at 12:36
  • $\begingroup$ @Astik Generally we expect the person who asks the question to do their own background research. If you "came across this question after reading some articles," those articles are a good place to start looking for links (or are good links themselves). $\endgroup$ – rob Nov 20 '19 at 15:39
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Interference depends on the wavelength associated with the momentum of the center-of-mass.

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  • $\begingroup$ By the center of mass, do you mean average of position distribution? Cause I don't see how we can have a center of mass for electrons or photons. $\endgroup$ – NiRVANA Nov 20 '19 at 12:23
  • $\begingroup$ Are you familiar with "Separation of the Center-of-Mass Motion" in classical mechanics or non-relativistic QM? $\endgroup$ – Keith McClary Nov 20 '19 at 15:04
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Astik,

The wavefunction describes the entire system, not individual particles separately. In order to find the wavefunction of a buckyball you calculate the buckyball's Hamiltonian and, in that step, you take into account all the relevant interactions (mostly electrostatic) between the nuclei and electrons. Only in the case there is no interaction you can describe each particle individually, but clearly, this is not the case here.

So, in the context of a two slit experiment, the buckyball behaves as a single entity, not as a stream of elementary particles. The interference is a result of the de Broglie wavelength associated with the molecule.

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  • $\begingroup$ So, basically, when I write down the hamiltonian, it will have as many degrees of freedom as twice the sum of num of electrons, protons, (neutrons also, if gravity or nuclear force is included?). And then, when I solve it, I shall get a wavefunction for the entire buckyball with some particular(singular) wavelength? $\endgroup$ – NiRVANA Nov 20 '19 at 12:30
  • $\begingroup$ I mean, even simple one or two-electron systems have wavefunctions of varying wavelengths(combination of eigenstates). So, if I were to pass them(without observation of course), they should show interference pattern that arises from interference of all those possible wavelengths, giving me a smear rather than distinct lines. $\endgroup$ – NiRVANA Nov 20 '19 at 12:33
  • $\begingroup$ You can look at this paper: "Wave-particle duality of C60 molecules" researchgate.net/publication/…. They used hot molecules, so there were many excited states. There was even a significant amount of slightly different molecules (different C isotopes). This did not significantly alter the pattern. The de Broglie wavelength depends on mass so probably the mass differences are too small to matter. $\endgroup$ – Andrei Nov 20 '19 at 13:22

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