sampleexam2

# sampleexam2 - Physics 604 Midterm#2 Fall 10 Dr Drake 1(40...

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Physics 604 Midterm #2 Fall ‘10 Dr. Drake 1. (40 pts) The modified spherical Bessel equation is given by z 2 y 00 + 2 zy 0 - [ z 2 + n ( n + 1)] y = 0 (a) Find the lowest order behavior of the solutions as z 0. Show that the solutions are linearly independent. Identify values of n for which they are not linearly independent and also calculate the solutions for this special value of n . (b) Calculate the behavior of the solutions for z large. Hint: To put the equation in standard form take y = f/z p and solve for p. 2. (60 pts) The temperature in a one-dimensional medium satisfies a diffusion equation: ∂T ∂t - D 2 ∂x 2 T = 0 At t = 0, the temperature in the medium is given by T (0 , x ) = ( 0 x > 0 1 x < 0 (a) Solve for the space/time dependence of T ( x, t ) by FIRST completing a
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