MIT5_74s09_pset05

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ∂ ρ I = − i [ V , I ρ I ] , where the density matrix in the interaction picture is defined as ∂ t h ρ = U † ρ U . I 0 S 0 a) How do you express the expectation value of the operator A in terms of ρ I ? b) The time development of ρ I can be obtained by integrating the equation of motion. Use the first-order solution to the differential equation for ρ 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 〉 ε a 〈 a| + |b 〉 ε b 〈 b| in which the dipole operator couples the two states: μ = |a 〉 μ ab 〈 b| + |b 〉 μ ba 〈 a|. What is the form of ρ eq ? What is the matrix form of U ? Show that your result is consistent with the Schrödinger representation 2 R ( ) t = 2 ∑ p n sin ω jn t A jn h n, j 5.74, Problem Set #5 Page 2 2. Vibrational relaxation in a triatomic We’ll examine the process of vibrational relaxation commonly found in triatomic molecules,...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online