## Physics Questions People Ask Fermilab

Double Slit

I am interested to know if there has been an experiment involving proton beams to compare to electron beam and twin slit experiments. I would also like to know if the incident areas of proton beams in a slit experiment are the same as those in a corresponding electron experiment, or it the areas of incident are different for the two types of particles. Since electrons exibit wave behaviour in a twin slit experiment, I would like to know if protons exibit the same behaviour, which I am sure they do, and if the slits are moved apart, at what distance of separation the beams of electrons stop finding the slits compared to the same study done with proton beams. If they are the same, then the wavelike properties would be due to their properties of charge, and if they are different, which I am sure they are, they would be due to the mass of the particle, the area being covered by the proton being larger. Would you please direct this e-mail to the right department, or in lieu of that direct me to the proper source for an answer to my question.

Thank you.
Randy Rivard

Dear Randy,

Excellent question although I don't know offhand of any experiments. I bet there are but I also bet you will find them on the web faster than I can. I will give you the resource I usually start with although it may be too recent:

I will also look around with Altavista, etc.

What I do know from basic quantum mechanics is that you can describe the proton as a wavefunction just as you can describe the electron. For a low current beam, you can usually use the "plane-wave approximation" which means you assume the particle is just flying in a straight line through space without interactions.

Then the wave function is just:

W = exp(i*[p.r - Et]/(hbar))

in other words, p = momentum vector, r = radius vector, i = sqrt(-1), E = energy, t = time, hbar = 1.022x10-34 Joule-sec. You can use this to quantify how the particle propagates through space as a function of time. You can also use superpositions of two wavefunctions at different distances of separation to describe your interference phenomena.

Notice a free wavefunction has no mention of charge or mass explicitly. Once you get it going at a certain fixed momentum-energy, who cares what charge or mass it has, as long as it does not interact with another particle. Basically what you are doing is splitting up the concepts of interaction via a force and quantum mechanical interference. If your wavefunctions are large but the force is short range then you can use this approximation.

For example, Bose-Einstein condensation has nothing to do with attractive forces per se (such as electromagnetism), it is purely exploiting the atoms or photons wanting to be in the same state. This is one reason why it is a purely quantum mechanical phenomenon which has no classical analog.

Does this make sense? Please let me know if you have any questions about it since it is quite an important concept in the understanding of physics.

Sincerely,

Glenn Blanford, PhD
Fermilab Public Affairs

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