MIT5_74s09_pset05

MIT5_74s09_pset05 - MIT OpenCourseWare http://ocw.mit.edu...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 5.74, Problem Set #5 Spring 2009 Due Date: April 6, 2009, 12pm 1. Density Matrix Description of the Linear Response Function In problem set 2 you showed that the equation of motion for the density matrix in the interaction picture is I = i [ V , I I ] , where the density matrix in the interaction picture is defined as t h = U U . I 0 S 0 a) How do you express the expectation value of the operator A in terms of I ? b) The time development of I can be obtained by integrating the equation of motion. Use the first-order solution to the differential equation for I above to obtain a density matrix expression for the linear response function. c) Explicity evaluate the expression in (b) for the electric dipole interaction of a field with a two level system H = |a a a| + |b b b| in which the dipole operator couples the two states: = |a ab b| + |b ba a|. What is the form of eq ? What is the matrix form of U ? Show that your result is consistent with the Schrdinger representation 2 R ( ) t = 2 p n sin jn t A jn h n, j 5.74, Problem Set #5 Page 2 2. Vibrational relaxation in a triatomic Well examine the process of vibrational relaxation commonly found in triatomic molecules,...
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MIT5_74s09_pset05 - MIT OpenCourseWare http://ocw.mit.edu...

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