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PS4 - Chem 442 Homework Set#4 DUE Saturday November 8 2008...

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Problem Set #4 - 1 - Chem 442 Homework Set #4 DUE: Saturday, November 8, 2008 1) In lecture 9, I introduced two new states for the particle on a ring: ( ) ( ) 1 1 cos and sin n n n n θ θ π π + Ψ = Ψ = a) Prove statements A and B on slide 5 of lecture nine. That is, prove that these two wavefunctions for the particle on a ring are eigenfunctions of the Hamiltonian. 2 2 2 ˆ Recall: H=- 2 d I d θ = b) Prove statement C on the same slide. That is, prove that these two wavefunctions are normalized. c) Find the probability that a particle in state n + Ψ is in the first quarter of the ring. Does this probability depend on n? d) Determine <L z > n , <L z 2 > n and σ Lzn for ψ n+ ( θ ). 2) Consider the ground state wavefunction for the harmonic oscillator.
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