Department of PhysicsProf. R. BundschuhThe Ohio State UniversityNinth Problem Set for Physics 847 (Statistical Physics II)Winter quarter 2004Important date:Mar 16 9:30am-11:18am final examDue date:Tuesday, Mar 924. Two-level bosons8 pointsAn ideal Bose-Einstein gas consists of non-interacting bosons of massmwhich have an internaldegree of freedom which can be described by assuming, that the bosons are two-level atoms.Bosons in the ground state have energyE0=p2/2m, while bosons in the excited state haveenergyE1=p2/2m+ Δ, wherepis the momentum and Δ is the excitation energy. Assumethat ΔkBT.a) Find an equation for the Bose-Einstein condensation temperatureTcfor this gas of two-level bosons. (Hint: this equation may not be so easy to actually solve since it involvesTcand exp(-βΔ) = exp(-Δ/kBTc) at the same time.)b) Does the existence of the internal degree of freedom raise or lower the condensationtemperature?
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Fundamental physics concepts, Fermi energy, Fermi, Two-dimensional Fermi gas