Let's suppose we have a Boson Non-interacting gas under an Harmonic potential so(adsbygoogle = window.adsbygoogle || []).push({});

[tex] V(x)= \omega (k) x^{2} [/tex]

the question is if we know what the Partition function is [tex] Z= Z (\beta ) [/tex] we could obtain the specific Heat, and other important Thermodinamical entities...but could we know what the "dispersion relation" w(k) for k real is? , i have looked several books about "Solid State" but i don't find any info about how to get dispersion relations using partition functions or similar..or if we can find an Integral or differential equation for the w(k)..thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Boson gas

**Physics Forums | Science Articles, Homework Help, Discussion**