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set9 - Department of Physics The Ohio State University Prof...

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Department of Physics Prof. R. Bundschuh The Ohio State University Ninth Problem Set for Physics 847 (Statistical Physics II) Winter quarter 2004 Important date: Mar 16 9:30am-11:18am final exam Due date: Tuesday, Mar 9 24. Two-level bosons 8 points An ideal Bose-Einstein gas consists of non-interacting bosons of mass m which have an internal degree of freedom which can be described by assuming, that the bosons are two-level atoms. Bosons in the ground state have energy E 0 = p 2 / 2 m , while bosons in the excited state have energy E 1 = p 2 / 2 m + Δ, where p is the momentum and Δ is the excitation energy. Assume that Δ k B T . a) Find an equation for the Bose-Einstein condensation temperature T c for this gas of two- level bosons. (Hint: this equation may not be so easy to actually solve since it involves T c and exp( - β Δ) = exp( - Δ /k B T c ) at the same time.) b) Does the existence of the internal degree of freedom raise or lower the condensation temperature?
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