Unformatted text preview: value of the angular momentum L? 7. Prove that the operator for the x component of orbital angular momentum is given by ( 29 ( 29 ( 29 ( 29 ∂ ∂ + ∂ ∂-= ϕ θ sin cos θ cos θ sin i L x H . 8. Consider a model of an electron as a tiny uniform sphere of size 10-18 m corresponding to the experimental limit on possible electron structure. Suppose that the electron intrinsic angular momentum is due to the spinning motion of a sphere with an angular frequency ω . Calculate the value of ω . Explain why this is a “bad” model of electron spin. 9. If you modeled the nucleus of hydrogen as a 1-D particle in a box with the distance between the walls of approximately 1 fm, what would be the energies of the first four states? 10. Assuming an electron is trapped in a 2-D square box whose sides are 1 nanometer. What are the energy values of the four lowest states?...
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- Spring '11
- Work, orbital angular momentum