In section 7.1 of his statistical mechanics, Pathria derives the formula ## N_e=V\frac{(2\pi m k T)^{\frac 3 2}}{h^3}g_{\frac 3 2}(z) ## where ## \displaystyle g_{\frac 3 2}(z)=\sum_{l=1}^\infty \frac{z^l}{l^{\frac 3 2}} ## and ## z=e^{\frac \mu {kT}} ##. This formula gives the number of particles that are not in the ground state w.r.t. the temperature.(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Problem with Bose-Einstein Condensation

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - Problem Bose Einstein | Date |
---|---|

I Cosmological constant problem | Mar 10, 2018 |

I Some (unrelated) questions about the measurement problem | Mar 9, 2018 |

I Spin and polarization basis problem? | Jan 18, 2018 |

I The Rabi problem | Jan 12, 2018 |

Problem understanding a statement in Bose Statistics | Aug 15, 2008 |

**Physics Forums - The Fusion of Science and Community**