Why Cannot I Factorize the Partition Function?

[Frank Einstein]

Hi everibody, the other day in a stadistical physics lesson we were studyng Fermi Dirac and Bose Einstein stadistics and comparing it to the classical Maxwell Boltzmann's.

We learned that in the quantum stadistics for indistinguishable particles the partition function of the whole system couldn't be written as the multiplication of the partition function of all the single particles of the system as we used to do when we were working in the classical limit.

So, can please anybody tell me if there is a physical reason why I can't write the partition formulal for Bose Einstein's and Fermi Dirac's stadistic as ∏(z_n)?

Thanks for reading.

 

[mfb]

The wavefunction has to be symmetric under exchange of two identical bosons, and antisymmetric under exchange of two identical fermions - otherwise you cannot reproduce the observed statistics. With a factorized partition function this does not work.

 

[Frank Einstein]

Thank you very much for your anwser.
By the way, can you point me to a book where whis is treated?

 

[mfb]

This should be covered in every book about quantum mechanics.

 

[DrDu]

However, while it is not possible to factorize the canonical partition function, it is possible to factorize the grand canonical partition function.