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I have seen many exercises such as "A 100kg rugby player running at 5m/s charges at you. Calculate his wavelength". Is it really accurate to say things like this for any non-single particle? In other words, does the rugby player have a single wavelength, the wavelength of the rugby player(he would be made of a single wave), or do all the particles he is made of have individual wavelengths(he would be made of trillions of waves, rotating in different directions, orbiting atoms etc)?

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  • $\begingroup$ Diffraction experiments with Buckyballs say yes. $\endgroup$ – Jon Custer May 1 '20 at 18:28
  • $\begingroup$ ...Buckyballs yes, but what does it mean to talk about the wavelength of an assembly of smaller particles when the wavelength of the whole assembly is many orders of magnitude smaller than distances between the component particles? You can calculate it, but that doesn't make it physically meaningful. $\endgroup$ – Solomon Slow May 1 '20 at 18:45
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If an object made of $N$ particles has a wavefunction (i.e. is in pure state), then its wavefunction is generally a function of $3N$ parameters (ignoring spin): each particle has 3 degrees of freedom. So, the wavefunction would be

$$\psi(\vec r_1,\vec r_2,\dots,\vec r_N).$$

But if the object moves in free space, then its momentum is conserved, and thus we can (for an eigenstate) separate the wavefunction describing motion of the center of mass of the object. Then

$$\psi(\vec r_1,\vec r_2,\dots,\vec r_N)=\exp(i\vec K\vec R)\phi(\vec r_1-\vec R,\vec r_2-\vec R,\dots,\vec r_N-\vec R),$$

where $\vec K$ is the wave vector of the center of mass (i.e. object as a whole), $\vec R$ is its position. And now $\lambda=\frac{2\pi}K$ is the de Broglie wavelength one is supposed to calculate in the exercises you mentioned.

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