Many Boson Wavefunction (Non-Interacting)

[Master J]

For a system of N bosons that are non interacting, the wavefunction is given by:


SQRT[1/N!.n_1!.n_2!.n_3!...] SUM P. A_1.A_2.A_3...A_N


Where the sum runs to N! and the P is the permutation operator, swapping 2 particles at a time. n_i is the number of particles in the nth energy state, and A_i is the ith single particle wavefunction.


I can't figure out where the normalization factor comes from? I just can't seem to logically get it out from normalization...could someone explain this perhaps?

Also, if particles are indistinguishable, can one still tell HOW MANY particles are in a given energy state?

 

[azntoon]

The normalization factor comes from the fact that the system of N bosons is normalized. This means that the probability of finding any particle in any state must add up to 1. The normalization factor is a mathematical tool which ensures that this condition is satisfied. Yes, one can still tell how many particles are in a given energy state if they are indistinguishable. The number of particles in a given energy state can be determined by summing up the number of particles in each single particle wavefunction A_i.