Question on de Broglie wavelength

[broegger]

When textbooks introduce the de Broglie wavelength of a particle they always ask you to calculate the wavelength of a macroscopic object like a football or something. Then they conclude: "Since the wavelength of ordinary objects like footballs are only 0.00001 nm (or whatever) quantum mechanics doesn't manifest itself in the everyday world."

Here is what I don't understand: Isn't the formula $$\lambda = h/p$$ only applicable to single particles, like electrons and protons. Can you just apply it to multi-particle systems like footballs??

I would think that the wavelength of a football must be some kind of superposition of the wavelengths of the single particles making up the football - which is too complicated to even consider. Thus I don't think it makes sense to talk about de Broglie wavelength for footballs, hats or cupcakes.

I'm aware that the wave nature of particles isn't noticeable in our everyday, but I think this is a bad argument!

 

[ZapperZ]

When textbooks introduce the de Broglie wavelength of a particle they always ask you to calculate the wavelength of a macroscopic object like a football or something. Then they conclude: "Since the wavelength of ordinary objects like footballs are only 0.00001 nm (or whatever) quantum mechanics doesn't manifest itself in the everyday world."

Here is what I don't understand: Isn't the formula $$\lambda = h/p$$ only applicable to single particles, like electrons and protons. Can you just apply it to multi-particle systems like footballs??

I would think that the wavelength of a football must be some kind of superposition of the wavelengths of the single particles making up the football - which is too complicated to even consider. Thus I don't think it makes sense to talk about de Broglie wavelength for footballs, hats or cupcakes.

I'm aware that the wave nature of particles isn't noticeable in our everyday, but I think this is a bad argument!

In principle, the deBroglie wavelength can be applied to anything. It isn't just for "single particle", or else there's no explanation why something as large as a buckyball (C60 and C70 that are roughly 200 times larger than a proton) can undergo interference and quantum tunneling. A buckyball is certainly not a single-particle.

Zz.

 

[broegger]

But the wavelength of a football must somehow be related to the wavelength of it's constituent particles?

 

[ZapperZ]

But the wavelength of a football must somehow be related to the wavelength of it's constituent particles?

That, we don't know, because to be able to know that, the whole object must be coherent with all its constituents. One can also argue that a proton should be considerent only via its quark content. Yet, it works fine if we consider it as an object with a single mass rather than the mass of its individual constituents.

Besides, if they are all traveling at relatively the same velocity, the momentum adds up nicely to represent the whole object as one "particle".

Zz.

 

[broegger]

I think this answers my question, thanks... Still; are we absolutely positive that it even makes sense to talk about wavelength for macroscopic objects?

 

[ZapperZ]

I think this answers my question, thanks... Still; are we absolutely positive that it even makes sense to talk about wavelength for macroscopic objects?

In depends on your "sense".

Zz.