Unformatted text preview: x, t ) in quantum mechanics: i ∂u ∂t = ∂ 2 u ∂x 2 Use separation of variables to show that this can have travelling waves solutions, i.e. that u ( x, t ) can look like e i ( kxwt ) , where k and ω are constants (which is equivalent to sin( kxωt ) and cosines). 3. Show that Laplace’s equation ∇ 2 φ = 0 in 2D cylindrical coordinates for φ = φ ( r, θ ) leads to Bessel’s equation (Kreyszig Section 5.5 Eq 1, with ν = 0) in one of the variables. What is the other ODE which results?...
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This note was uploaded on 07/23/2008 for the course MATH 405 taught by Professor Belmonte during the Fall '06 term at Penn State.
 Fall '06
 BELMONTE
 Calculus, Addition

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