486_HW9 - Physics 486 Homework Set 9 Due 1 Understanding...

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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 x-axis, ii) |Y| as a function of θ in polar co-ordinates, where the angle represents θ and the radius represents |Y| and iii) |Re[Y]| as a function of ϕ in polar co-ordinates, 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 three-dimensions (projected onto your paper, of course, with the physical x-, y- and z-axes marked). your paper, of course, with the physical x-, y- and z-axes 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.

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486_HW9 - Physics 486 Homework Set 9 Due 1 Understanding...

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