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3890ps9_10 - Chem 3890 Physical Chemistry I Fall 2010...

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Chem 3890 Physical Chemistry I Fall 2010 Chemistry 3890 Problem Set 9 Fall 2010 Due: in class, Friday, November 12 Last revised: November 6, 2010 Additions/corrections: Problem 1 A rigid rotor (particle on a sphere) is prepared at time t = 0 in the state ψ = 1 2 [ Y 0 , 0 + Y 1 , 0 ] . (1) 1. Verify that the state ψ is normalized. 2. Write down an expression for the state of the system Ψ( t ) at time t , given that the system Hamil- tonian is the free rotor Hamiltonian ˆ H = ( B/ planckover2pi1 2 ) ˆ L 2 , B planckover2pi1 2 / (2 μr 2 ). 3. Write down an expression for the density ρ = Ψ * Ψ at time t , given that the system Hamiltonian is the free rotor Hamiltonian ˆ H = ( B/ planckover2pi1 2 ) ˆ L 2 . Your expression should be a function of the angle θ and the time t , and should be manifestly real. Does ρ depend on φ ? 4. Show that ρ is a periodic function of t , and determine the period T p . Determine the value of the period T p for the diatomic molecule HCl, assumed to be a rigid rotor.
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