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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 ( x ) exp(i E t/ h ). Determine the probability (in the Form oF an integral) oF nding 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 , , and h . (c) Calculate the variance 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(z 2 ) = 1 2 r 3 . 3. Show that the three stationary wave Functions 1 ( x ) = C 1 exp(x 2 ), 2 ( x ) = C 2 x exp(x 2 ), and 3 ( x ) = C 3 (4 x 21) exp(x 2 ) are all mutually orthogonal. Claudia Eberlein, 11 Jan 2005 1...
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This note was uploaded on 08/12/2008 for the course PHYS 252 taught by Professor Pocanic during the Spring '02 term at UVA.
 Spring '02
 POCANIC
 Physics, mechanics

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