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Consider an ideal gas of bosons with internal degrees of freedom. Suppose that, besides the ground state with zero en- ergy (εo = 0), we have to take into account the first excited state, with internal energy ε1 > 0. In other words, assume that the energy spectrum is given by
where σ = 0, 1. Obtain an expression for the Bose–Einstein condensation temperature as a function of the parameter ε1.
Physics
In the grand-canonical formalism, above the temperature of condensation, the number of bosons is given by
In the thermodynamic limit, we write
At the temperature of the Bose-Einstein condensation (z→ 1), we have
from which we may (numerically) obtain TO (which is smaller than the corresponding value with x1 = 0)
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