Unformatted text preview: ≤ x ≤ L. ψ 2 ( x ) = r 2 L sin ( 2 πx L ) (1) The expectation value of x is L 2 . Sketch the square of the wave function and show where the particle is most likely to be. Why do these points diﬀer from the expectation value of x? (+ 4 pt) The most likely positions are around x = L 4 and x = 3 L 4 . It is clear from the plot of the probability density that it maximized around these positions. However, the symmetry forces the expectation value of position to L 2 . Some possibly useful equations: E n = n 2 h 2 8 mL 2 , h = 2 π ¯ h E photon = hf = hc λ < x > = R L ψ * xψ dx 1...
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 Spring '08
 Wu
 Work, Photon, Fundamental physics concepts, expectation value, ID Section InClass

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