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# ps9 - Physics 115A Ninth Problem Set Harry Nelson Office...

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Unformatted text preview: Physics 115A Ninth Problem Set Harry Nelson Office Hour None this week! TA: Antonio Boveia Office Hours M 9-10am, Fr 1-3pm PLC Grader: Victor Soto Office Hours Th 11:00-12:30pm PLC due Monday, March 10, 2003 1. In this problem find the propagator and interpret the results for the simplest 2-state system. Your understanding of this problem can be applied to Magnetic Resonant Imaging, neutrino oscillation, and CP violation, among other physics problems. For the 2-state system here, imagine that the eigenvalues are: E 1 = + ¯ hω 2 , E 2 =- ¯ hω 2 , where ω can be thought of simply as a parameter related to the energy eigenvalues. The propagator, U ( t, 0), is then: U ( t, 0) = | ¯ hω/ 2 ) e- iωt/ 2 ( ¯ hω/ 2 | + | - ¯ hω/ 2 ) e iωt/ 2 (- ¯ hω/ 2 | (a) Find the matrix that represents the Hamiltonian, H , in the eigenbasis of H . (b) Find the matrix that represents the propagator U ( t, 0) in the eigenbasis of H ....
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ps9 - Physics 115A Ninth Problem Set Harry Nelson Office...

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