Physics - Statistical Mechanics - Boltzmann distribution and partition function - Partition Function Problems

6 problems. P1: 'Three-level system with energies 0, ε, 2ε. Partition function Z = 1 + e^(-βε) + ___' (e^(-2βε)). P2: 'At k_BT = ε (βε = 1): Z = 1 + e⁻¹ + e⁻² = 1 + 0.368 + 0.135 = ___' (1.503). P3: 'Probability of ground state: P₀ = 1/Z = ___' (0.665). P4: 'Probability of highest state: P₂ = e⁻²/Z