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: ()()11cosand sinnnnnθθππ+−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. 222ˆRecall: H=-2dI dθ=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+Ψis in the first quarter of the ring. Does this probability depend on n? d) Determine <Lz>n, <Lz2>nand σLznfor ψn+(θ). 2) Consider the ground state wavefunction for the harmonic oscillator.
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