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ME501HW1F2011

ME501HW1F2011 - 1 ME 501 Homework#1 Due Friday Prof...

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1 ME 501 Homework #1 Due Friday, September 16, 2011 Prof. Lucht (E-mail address: [email protected] ) Note: A useful table of integrals in posted on the class website. 1. Laurendeau, Problem 3.2, p. 147. 2. A particle of mass m is constrained to move along the x-axis in the region 0 x L . The normalized wavefunction for the particle is given by ( , ) ( ) ( ) sin exp ( , ) , x t x T t L n x L i t x L x t x x L h n m L F H I K F H I K 2 0 0 0 8 1 1 1 2 1 2 2 The uncertainty B in the determination of the value of a dynamical variable B is given by the square root of the variance, B B B 2 2 . For a particle with quantum number 1 3 n , determine the value of the product x p x . Is this result consistent with Heisenberg's uncertainty principle? 3. A particle confined along a line between x = 0 and x = L is in a "mixed" quantum state, i.e., a linear superposition of the eigenstates A and B with quantum numbers 1 3 A n and 1 5 B n , respectively.
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