542-problem-7 - 1 2 3 1 p p p + + = . a) Show that the...

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Chem. 542 Assignment by Nancy Makri PROBLEM 7 Consider a two-state system, for which the eigenstates of the Hamiltonian are ( 29 ( 29 1 2 1 1 , 2 2 L R L R Φ = + Φ = - where , L R are orthonormal left- and right-localized states. We define the density operator 1 2 3 1 1 ˆ p L L p R R p ρ = + + Φ Φ , where the coefficients are positive numbers and
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Unformatted text preview: 1 2 3 1 p p p + + = . a) Show that the trace of the density operator is 1. b) Calculate the eigenstates and eigenvalues of the density operator. Express the density operator in terms of its eigenstates and eigenvalues....
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This note was uploaded on 02/08/2012 for the course CHEM 542 taught by Professor Gruebele during the Spring '08 term at University of Illinois, Urbana Champaign.

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