Indistinguishability Of Particles

[Fowler_NottinghamUni]

Hi, I am a student at Nottingham University England. I am currently studying for a degree in Physics, doing a second year module in Quantum Mechanics. I was just wondering if anyone could explain the indistinguishability of particles.

 

[ZapperZ]

Hi, I am a student at Nottingham University England. I am currently studying for a degree in Physics, doing a second year module in Quantum Mechanics. I was just wondering if anyone could explain the indistinguishability of particles.

Indistinguishability is the foundation of quantum statistics. In QM, particles (and sometime even LARGE partices) can be described by the Schrödinger wave equation. This means that these are not classical particles, but can have some "spread", both in real space and momentum space.

Now, if these particles are, on average, far enough apart, the "spreading" of what or who they are doesn't come into play. We can accurately describe them as classical particles. However, if they interact with each other very often, or are in very close proximity to each other so much so that their wavefunctions begin to overlap significantly, then something unusual happens. QM says that in this situation, you can no longer identify one from the other, and your ability to track one particle unambiguously is gone.

Now this is different than, let's say, having 20 identical-looking red balls. While they all look the same, you can STILL make out that they are twenty DISTINCT red balls. If you have a good eye, you can still follow one red ball as I shake all of them. In the QM indistinguishable case, you don't even see 20 read balls, but rather a fuzzy red glob. Their individuality is no longer there. When this happens, a whole set of quantum statistics kicks in, and this is where you get the fermi-dirac and bose-einstein statistics.

Zz.

 

[Fowler_NottinghamUni]

Cheers

Thanks that's brilliant!

 

[HallsofIvy]

Feynman had a lovely explanation- he pointed out that if you look at electron-positron creation, drawing it with time as an additional axis, you can think of the positron as an electron going backwards in time- that's why all electrons are indistiguishable: there's really only one electron bouncing back and forth in time!

 

[selfAdjoint]

Feynman had a lovely explanation- he pointed out that if you look at electron-positron creation, drawing it with time as an additional axis, you can think of the positron as an electron going backwards in time- that's why all electrons are indistiguishable: there's really only one electron bouncing back and forth in time!

This concept is usually fathered on Feynmann, but according to him it was Wheeler who phoned him with the idea. Feynman initially thought it was a little too crazy.

 

[Fowler_NottinghamUni]

Energy Level diagrams

Hi again, i am having a little bit of trouble with a question my professor has set. He asks us to consider the 3p4s configuration in the L-S coupling and j-j coupling approximations and sketch the energy levels schemes that characterise the two. Does this involve finding exchange and coulomb integrals separately or is this a standard result for J an K I am a little confused (again). Many thanks.