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Unformatted text preview: M , and chemical potential μ . d) The surface is exposed to an ideal gas of the atoms at some pressure P and the same temperature T as the surface. Calculate the fraction N/M of adsorbed atoms as a function of the pressure P of the ideal gas and the temperature T of the system. (Hint: in thermodynamic equilibrium the chemical potentials of the adsorbed atoms and the atoms in the ideal gas have to be equal.) 17. Density operator 10 points a) In a two-dimensional Hilbert space an operator ˆ ρ is given by the matrix ˆ ρ = 1 2 ˆ 1 + a 1 a 2 a 3 1-a 1 ! . Determine for which values of the three complex parameters a 1 , a 2 , and a 3 this operator is a density operator. ±or which values of the three parameters is it a pure state? b) Prove that for a hermitian Hamiltonian ˆ H the operator ˆ ρ ≡ e-β ˆ H / tr e-β ˆ H is a density operator. 1...
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This note was uploaded on 07/17/2008 for the course PHYS 847 taught by Professor Bundschuh during the Winter '04 term at Ohio State.
- Winter '04