Next: Understanding the periodic Table
Up: Quantum Mechanics of Atoms
Previous: Symmetric / antisymmetric wave
Consider a twoparticle noninteracting fermion system. The ``noninteracting'' qualifier
implies the twoparticle wave function can be written as the product of two
single particle wave functions.
These can be written as

(58) 
or

(59) 
where and label two different single particle
states. Because we cannot distinguish between the particles, we cannot know
which of or describes the system. Consequently we have to consider
the system as being in some linear combination of and .
There are only two correctly normalised combinations possible.

(60) 
and

(61) 
In the case of Fermions, if , then , implying that no two
fermions can occupy the same state. By considering the form of wavefunction
for a system of identical particles, we have arrived almost effortlessly at
Pauli's Exclusion Principle ! This result will be shown soon to account for
the structure of atoms and metals. Its tremendous significance implies
that the wavefunction, even though it is not directly observable, must nonetheless
be an object of tremendous physical, not only mathematical, validity.
Clearly, bosons do not obey this principle, and many particles of this type
may be found in the lowest (ground) state. Bosonic systems display curious
properties such as super conductivity.
Next: Understanding the periodic Table
Up: Quantum Mechanics of Atoms
Previous: Symmetric / antisymmetric wave
Simon Connell
20041004