quiz 2 - Quiz 2 CHEM 482 September 30, 2009...

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Unformatted text preview: Quiz 2 CHEM 482 September 30, 2009 ______________________________ please print your name There are 25 total points on this quiz, as indicated in problems 1 - 3. There are no problems on page 1, just information that may be useful to you. - (,) Schrdinger Equation 1D TDSE separation of variables 1D TISE (, ) = () - / 2 2 2 () 2 =- + ()( ) = () 2 2 2 (,) 2 + ()(, ) QM Particle in a 1D Box: 0, 0 () = , < 0 > = = 8 2 2 2 2 0 Integration using spherical coordinates: = 2 sin ; (2 ) 4 all space: 0 , 0 , 0 2 2 () = - = 0 2 2 2 2 () = 2 - Integrals: - = 0 - = 0 2 2 sin() cos() = 3 - = 0 2 1 +1 2 2 1 ! 2 ( ) 2 ( > 0) 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) 2 Problem 1 (8 points) Briefly discuss (in words) the physical origin of quantization of the energy of matter by using a quantum mechanical particle in a one-dimensional infinite box as an example. (8 points)In this problem, assume the n's are the normalized eigenfunctions of the particle in a 1D box given on page 1. Determine the values of the following integrals (you should be able to do this by inspection). Also for each, indicate the meaning of the integral (i.e. what quantity is being calculated) and a brief justification for your answer. Problem 2 A. 2 2 = - B. 2 3 = - C. 2 2 = - D. 1 (- )1 = - 3 Problem 3 (9 points) A particle of mass m is trapped in a one-dimensional infinite box of width L. Its normalized wavefunction at time t = 0 is (, = 0) = + 1 2 1 4 - . 2 2 If you measure the energy of this single particle at t = 0, what are the possible results and what is the probability of obtaining each result? ...
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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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