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Unformatted text preview: 1 Problem 1 Do the onedimensional kinetic energy and momentum operators commute? If not, what operator does their commutator represent? KE = h 2 2 m d 2 dx 2 P = i h d dx 1.1 Solution This question requires calculating the commutator of the operators given. h KE, P i = h 2 2 m d 2 dx 2 i h d dx i h d dx h 2 2 m d 2 dx 2 = i h 3 2 m d 2 dx 2 d dx d dx d 2 dx 2 = i h 3 2 m d 3 dx 3 d 3 dx 3 = The operators commute; all done. 2 Problem 2 Given the following wavefunction, describing some quantum particle, ex panded in a basis of eigenfunctions of a location operator, = C left left + C right right + C top top + C bottom bottom NOTE :(the eigenfunction left is associated with an eigenvalue of LEFT, and so on for the other eigenfunctions) 2a. What is the probability of observing a value of TOP (before any ex plicit measurement is made). If we have a detector that measures the LEFT location, and a signal is detected there after a particle is projected towards the array of detectors: 2a. How would you write the expression for the wavefunction? 2b. What is the probability of observing a value of LEFT?...
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This note was uploaded on 02/02/2012 for the course CHEM 444 taught by Professor Dybowski,c during the Fall '08 term at University of Delaware.
 Fall '08
 Dybowski,C
 Physical chemistry, pH

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