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 twodimensional Hilbert space an operator ˆ ρ is given by the matrix ˆ ρ = 1 2 ˆ 1 + a 1 a 2 a 3 1a 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 ≡ eβ ˆ H / tr eβ ˆ H is a density operator. 1...
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 Winter '04
 BUNDSCHUH
 Physics, Thermodynamics, Fundamental physics concepts, Statistical Physics II, Department of Physics The Ohio State University

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