Unformatted text preview: x that a classical particle can reach iF it has the total energy E . (b) Assume that the wave Function oF the particle is the stationary state φ ( x ) exp(i E t/ ¯ h ). Determine the probability (in the Form oF an integral) oF ²nding the particle outside the region where classical motion can occur. By making an appropriate change oF variable in the integral you obtain, show that the answer is independent oF m , ω , and ¯ h . (c) Calculate the variance Δˆ x in the groundstate oF the system and compare it to the limits oF the classical motion. Useful integral: Z ∞∞ d z z 2 exp(αz 2 ) = 1 2 r π α 3 . 3. Show that the three stationary wave Functions φ 1 ( x ) = C 1 exp(x 2 ), φ 2 ( x ) = C 2 x exp(x 2 ), and φ 3 ( x ) = C 3 (4 x 21) exp(x 2 ) are all mutually orthogonal. Claudia Eberlein, 11 Jan 2005 1...
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 Spring '02
 POCANIC
 Physics, mechanics, problem sheet, groundstate wave function, Claudia Eberlein, classical motion, probability current density

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