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# HW7 - Homework#7 Your Name Due on Monday November 21 before...

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Homework #7 Y o u r N a m e : Due on Monday, November 21, before the lecture. Only two problems will be graded explicitly. 1) Find spherical coordinates for points with the following (x, y, z) coordinates: a) (1, 2, 0) b) (-1, 0, 3) c) (-1, -1, -1) 2) Find   y x L L , 2 3) a) Show that spherical harmonics are eigenfunctions of the operator 2 2 y x L L b) What are the eigenvalues? 4) a) If we measure L z of a particle that has angular momentum quantum number l = 2, what are the possible outcomes of the measurement? b) If we measure L z of a particle whose state function is an eigenfunction of the operator 2 L with eigenvalue 12 , what are the possible outcomes of the measurement? 5) At a certain time t , a particle has the state function ) , ( 1 2 2 Y Ne ar where N and a are constants. a) If L 2 of this particle would be measured at time t , what would be the outcome? Give a numerical answer. b) If L z of this particle would be measured at time t , what would be the outcome? Give a numerical answer.

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HW7 - Homework#7 Your Name Due on Monday November 21 before...

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