quiz 3 - Quiz 3 CHEM 482 October 14, 2009...

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Unformatted text preview: Quiz 3 CHEM 482 October 14, 2009 ______________________________ please print your name There are 25 total points on this quiz, as indicated in problems 1-2. There are no problems on page 1, just information that may be useful to you. 0, () = , = 82 2 2 QM Particle in a 1D Box: 2 = 0 < 0 > QM Harmonic Oscillator: () = = 1/4 1 2 () - /2 ! 2 where 2 = 0 1 2 2 2 1 = + 2 (1) and () = (-1) - 2 2 2 = (0) + Perturbation Theory: = (0) (0) 2 ( ) = 2 - Integrals: sin( ) cos( ) = - = 0 - = 0 2 2 (2 ) 4 3 - = 0 2 1 +1 2 2 1 ! 2 ( ) 2 ( > 0) 2 ( ) = - = 0 2 2 2 2 2 ( ) = 2 - = 0 4 - = 0 1 2 2 4 1 4 3 8 3 6 - 3 5 - (2 ) 4 4 2 (2 ) - - (2 ) 8 2 2 2 2 -1 8 3 (2 ) Problem 1 The unperturbed wavefunctions and associated energies of a particle in a one-dimensional infinite well of length L are provided on the first page. Suppose we introduce a small step of height in the potential energy. The step has a width of L/10 and is centered within the well (as depicted in the figure below). a. (8 points) Using perturbation theory, find the first order to the correction to the energy of the nth state. b. (8 points) Evaluate the first order energy correction for the ground state and first excited state. Compare the impact of the perturbation on the energies of these two states (i.e. compare the magnitude of the energy correction), and briefly discuss the physical origin of this result. Problem 2 a. (6 points) Define tunneling as it relates to quantum mechanics, and briefly discuss the physical origin of tunneling. b. (3 points)Are heavier or lighter particles more likely to tunnel? ...
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This note was uploaded on 03/03/2010 for the course CHEM 431 taught by Professor Pielak during the Spring '07 term at UNC.

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