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Unformatted text preview: Physics 486 Homework Set 9 Due: Nov 15, 2007 1) Understanding spherical harmonics. Consider four of the spherical harmonics Y , 1 1 Y , 2 Y and 2 2 Y (given in Griffiths, page 139). The first two parts of this problem involve visualization – feel free to use a plotting program or any references. (a) Plot each of these harmonics in three ways: i) Y as a function of θ , where θ lies along the xaxis, ii) Y as a function of θ in polar coordinates, where the angle represents θ and the radius represents Y and iii) Re[Y] as a function of ϕ in polar coordinates, where the angle represents ϕ and the radius represents Re[Y] (Re[Y] denotes the real part of Y). (Don’t worry about the normalization constant – the relative magnitude as a function of angles is what it important.) (b) Having plotted the above for each of the four spherical harmonics, use the latter two sets of plots to generate an image of Re[Y] in threedimensions (projected onto your paper, of course, with the physical x, y and zaxes marked). your paper, of course, with the physical x, y and zaxes marked)....
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This note was uploaded on 09/20/2010 for the course PHYS 486 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Staff
 Work, Quantum Physics

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