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It tells me the average energy is about u = Eo + (deltaE)e^(-B delatE) as t approaches 0, and u = (1/2)(Eo + E1) - (1/4)B(delataE)^2 as T approaches infinity. I was able to easily get the first term in these expressions, but how the second term is coming out I have no idea. I was trying taking a derivitive for a while, but I don't believe that that is the way to go. Does anybody have any ideas?

Thanks