Physics 604Midterm #2Fall ‘10Dr. Drake1. (40 pts) The modified spherical Bessel equation is given byz2y00+ 2zy0-[z2+n(n+ 1)]y= 0(a) Find the lowest order behavior of the solutions asz→0. Show that thesolutions are linearly independent. Identify values ofnfor which they arenot linearly independent and also calculate the solutions for this specialvalue ofn.(b) Calculate the behavior of the solutions forzlarge.Hint: To put the equation in standard form takey=f/zpand solve for p.2. (60 pts) The temperature in a one-dimensional medium satisfies a diffusionequation:∂T∂t-D∂2∂x2T= 0Att= 0, the temperature in the medium is given byT(0, x) =(0x >01x <0(a) Solve for the space/time dependence ofT(x, t) by FIRST completing a
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