Interference of two particles - how does it work?

[Anthus]

Hello,
I'm at this forum for some time, but that's my first post. Forum is so huge that I can't cope with reading even small part of it :)
My question is connected with interference in quantum mechanics. We have two particles passing through two different slits. They interfere - but what exacly does it mean? What kind of interact is it?
For water waves it seems simple, because their particles oscillate horizontally and when waves superimpose, it's intuitive what happen to them. But it's classical physics...

 

[f95toli]

It is very similar to interference of light (water waves is a bit of a bad example, since you then have a medium).
First of all, it is important to understand that there is no such thing as a "particle" in the classical sense in QM, e.g. an electron has properties that are sometimes best understood as "particle like" and sometimes -as in the case of interference- "wave like". The wavelength of a particle (known as de Broglie wavelength) is inversely proportional to its mass, which is why you rarely see this effect the macroscopic world; things that we can see with our bare eyes are simply too heavy for any of the "wave-like" properties to be visible.

Also, note that there is NO PARADOX; the particle-wave duality is perhaps strange but is "natural" in the context of QM, it is only when we try to understand it in terms of our everyday experience that it becomes confusing.

Hence, once you understand that all particles are also waves interference phenomena are nothing surprising. in some experiments interference has even been seen between very heavy (relatively speaking) object such as C60 molecules.

 

[lightarrow]

Hello,
I'm at this forum for some time, but that's my first post. Forum is so huge that I can't cope with reading even small part of it :)
My question is connected with interference in quantum mechanics. We have two particles passing through two different slits. They interfere - but what exacly does it mean? What kind of interact is it?
For water waves it seems simple, because their particles oscillate horizontally and when waves superimpose, it's intuitive what happen to them. But it's classical physics...

There is interference even if only one particle at a time passes through the slits.

 

[Anthus]

OK, thanks, so I must understood something wrong...
I thought that de Brogile wavelenght and wave-particle duality belong to classical physics and in QM we consider light only like an elementary particle... I've read too much about double-slit experiment :)
On the other hand, is it a false that de Broglie wavelenght is displaced by wave function (maybe in other interpretations of QM)?

 

[f95toli]

The de Broglie wavelenght is something "physical" in the sense that it is a measure of the wavelength of a particle of mass m.

A wavefunction is a mathematical construct which does not neccesarily have anything to do with waves (in fact, you do not even have to use wavefunctions in QM, density matricies can be used instead and describe exactly the same thing); you can write down a wavefunction for ANY system you can think of (including macroscopic systems).
The Schrödinger equation belongs to a class of mathematical partial differential equations called "wave equations" (which also includes PDEs for water waves), I guess this is where the name wavefunction comes from. Wavefunctions can also be written in terms of amplitudes and phases, but generally speaking you can't talk of the "physical size" of a wavefunction (except in problems where the position of something is actually involved).

 

[Anthus]

Thank you :)

 

[monish]

Hello,
I'm at this forum for some time, but that's my first post. Forum is so huge that I can't cope with reading even small part of it :)
My question is connected with interference in quantum mechanics. We have two particles passing through two different slits. They interfere - but what exacly does it mean? What kind of interact is it?
For water waves it seems simple, because their particles oscillate horizontally and when waves superimpose, it's intuitive what happen to them. But it's classical physics...

I am motivated to comment on your assertion that two particles pass through two slits and they interfere. I assume you are thinking of electrons. The peculiar thing about electrons is that two different electrons DON'T interfere with each other. If they did, a typical atom (other than hydrogen) would be a confused jumble of interfering charge waves, radiating chaotically as they interfere with each other. It is precisely because each electron interferes only with itself that an atom can be stable.

 

[ZapperZ]

Hello,
I'm at this forum for some time, but that's my first post. Forum is so huge that I can't cope with reading even small part of it :)
My question is connected with interference in quantum mechanics. We have two particles passing through two different slits. They interfere - but what exacly does it mean? What kind of interact is it?
For water waves it seems simple, because their particles oscillate horizontally and when waves superimpose, it's intuitive what happen to them. But it's classical physics...

You may want to read this thread:

https://www.physicsforums.com/showthread.php?t=73919

The interference pattern that we are familiar with is the single-particle interference, not two-particle interference. Two-particle interference almost never occurs and exhibit a different property (See the Mendel reference that I cited in that thread).

Zz.

 

[monish]

To ZapperZ: I was talking about electrons and it seems you are talking about photons. These cases are pretty different. If you allow the Schroedinger function of two different electrons to interfere, you get a real mess. But two light waves add up and cancel each other according to the normal classical laws. So I don't see why this doens't work down to the level of photons.

 

[lightarrow]

To ZapperZ: I was talking about electrons and it seems you are talking about photons. These cases are pretty different. If you allow the Schroedinger function of two different electrons to interfere, you get a real mess. But two light waves add up and cancel each other according to the normal classical laws. So I don't see why this doens't work down to the level of photons.

Two light waves is a thing, two photons is another.

 

[Viva-Diva]

It is very similar to interference of light (water waves is a bit of a bad example, since you then have a medium).
First of all, it is important to understand that there is no such thing as a "particle" in the classical sense in QM, e.g. an electron has properties that are sometimes best understood as "particle like" and sometimes -as in the case of interference- "wave like". The wavelength of a particle (known as de Broglie wavelength) is inversely proportional to its mass, which is why you rarely see this effect the macroscopic world; things that we can see with our bare eyes are simply too heavy for any of the "wave-like" properties to be visible.

Also, note that there is NO PARADOX; the particle-wave duality is perhaps strange but is "natural" in the context of QM, it is only when we try to understand it in terms of our everyday experience that it becomes confusing.

Hence, once you understand that all particles are also waves interference phenomena are nothing surprising. in some experiments interference has even been seen between very heavy (relatively speaking) object such as C60 molecules.

By the way if you read my post today you will realize that it has been even shown for a macroscopic object- a big silicon drop (1 million times larger than c60).
here is the link http://www.physorg.com/news78650511.html

thanks Viva Diva