- #1

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The maximum of ## g_{\frac 3 2}(z) ## happens at ## z=1 ## and is equal to ## \zeta(\frac 3 2) ##. So whenever ## z=1 ##, ## N_e ## reaches its maximum and any other particle has to go to the ground state and ## z=1 ## happens at any ## T<T_c ##.

My problem is with ## T>T_c ##. I can calculate ## N_e ## for any temperature which gives me the capacity of the excited states at the given temperature. Now I put ## N>N_e ## particles in the energy levels and so the excited states become full and the rest of the particles have to go to the ground state and I get Bose-Einstein condensation again, this time for ## T>T_c ## which can't be right because we're supposed to have condensation only for ## T<T_c ##.

What's wrong here?

Thanks