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quanlop93
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Homework Statement
Ground state energy is set at 0.
[tex]E_n=\left(1-\frac{1}{n+1}\right)\in[/tex] with no degeneracy [tex](\Omega(n)=1); (n=0,1,2...)[/tex]
Write down the partition function and look for its limit when [tex]kt \gg \in\\ kt \ll \in[/tex]
Homework Equations
The Attempt at a Solution
Partition function for this is [tex] Z=\sum_{n=0}^\infty e^{-\beta\left(1-\frac{1}{n-1}\right)\in}[/tex]
Consider Z when ##kt \ll \in## then ##\beta e \gg1## then ## e^{-\beta e} \rightarrow 0## This leads to the whole summation will go to 0. But we know that at low temperature, Z always goes to 1.
I have tried to calculate the summation but this series is divergent.
How can I change the calculation to reach Z =1?