# The difference between BOSONS and FERMIONS

1. Apr 15, 2008

### abdullahbameh

i have read and studyed that
1/ boson are identical particles having zero or integral spin and can not be distinguished because their wave function over lap and they do not obey Pauli Exclusion Principle means a huge number of bosons can exist inte same quantum state like photons.((EB))
1/ fermions are identical particles have odd half-integral( 1/2,3/2,.....) and can not be distinguished by because their wave function gets overlap and they obey Pauli Exclusion principle means two fermions can not exist ine same quantum state. ((FD))
like free electron in metal that conduct the current.

please any other difference and correct me if i am wrong.

2. Apr 15, 2008

### lbrits

Woosh!

Roughly, bosons can undergo Bose condensation. At sufficiently low temperature, they will mostly be in the same state (because they can).

Fermions can't do that, because they aren't allowed to be in the same state. So at low energy, they pile up, and obey a Fermi-Dirac distribution.

Both are indistinguishable particles, but it isn't because their wavefunctions overlap. You can have two fermions that are well separated in space, but you can't tell which is which. It is just a fundamental property.

One way to explain this is that, given two non-interacting particles with wavefunctions $$\psi_1(x)$$, $$\psi_2(x)$$, the wavefunction of the total system is either

$$\Psi(x_1, x_2) = \psi_1(x_1) \psi_2(x_2) + \psi_1(x_2) \psi_2(x_1)$$
or
$$\Psi(x_1, x_2) = \psi_1(x_1) \psi_2(x_2) - \psi_1(x_2) \psi_2(x_1)$$.

Thus $$|\Psi(x_1, x_2)|^2$$ measures the probability density of measuring a particle at $$x_1$$ and another one at $$x_2$$, but doesn't say which particle is which.

Last edited: Apr 15, 2008
3. Apr 16, 2008

### abdullahbameh

what make them stay in one state or more than one state is some kind of property inbulit in that particle or just because exclusion principle say so

4. Apr 16, 2008

### lbrits

Your question isn't very clear, but... the fact that the WF changes sign when you interchange two particles (fermions) or doesn't (bosons) is a fundamental property which either leads to the Pauli exclusion principle (fermions) or doesn't (bosons). The fact that bosons tend to bunch up in one state at low temperature, and fermions tend to pile up at low temperature, is a conclusion arrived at from statistical mechanics taking into account their identical nature and their bosonic/fermionic nature.