# Indistinguishability Of Particles

• Fowler_NottinghamUni
In summary: 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?This is a standard result for J and K. You would need to do a calculation to find the exchange and coulomb integrals.
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.

Fowler_NottinghamUni said:
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 Schrodinger 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.

Cheers

Thanks that's brilliant!

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!

HallsofIvy said:
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.

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.

## 1. What is the principle of indistinguishability of particles?

The principle of indistinguishability of particles states that two or more particles of the same type are considered identical and cannot be distinguished from one another based on their physical properties, such as mass, charge, or spin.

## 2. How does the principle of indistinguishability apply to quantum mechanics?

In quantum mechanics, particles such as electrons, protons, and neutrons are described by wave functions that determine their probability of being in a certain state. The principle of indistinguishability states that the wave function must be symmetric for identical particles, meaning that it remains unchanged if the particles are exchanged. This leads to the concept of quantum states being occupied by multiple identical particles at the same time, known as quantum superposition.

## 3. Can particles with different physical properties be considered indistinguishable?

No, the principle of indistinguishability only applies to particles with the same physical properties. For example, an electron and a proton are considered distinguishable particles because they have different charges and masses. However, two electrons are considered identical and indistinguishable from one another.

## 4. How does the principle of indistinguishability affect the behavior of particles in a system?

The principle of indistinguishability leads to the phenomenon of quantum statistics, which describes the behavior of particles in a system. Depending on their spin, particles can either follow the rules of Bose-Einstein statistics or Fermi-Dirac statistics. This affects the way particles interact and allows for the formation of certain states, such as Bose-Einstein condensates and electron shells in atoms.

## 5. Are there any exceptions to the principle of indistinguishability?

There are certain cases where particles may appear to violate the principle of indistinguishability, such as in the case of entangled particles. However, these exceptions can still be explained by quantum mechanics and do not disprove the principle as a whole. Additionally, particles with different internal structures, such as quarks, may also be considered distinguishable even if they have the same physical properties.

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