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

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# Boson gas

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