7 - MIT Department of Chemistry 5.74 Spring 2004...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
p. 48 IRREVERSIBLE RELAXATION We want to study the relaxation of an initially prepared state. We will show that first-order perturbation theory for transfer to a continuum leads to irreversible transfer—an exponential decay—when you include the depletion of the initial state. The Golden Rule gives the probability of transfer to a continuum (for a constant perturbation): +, 2 k kk k 0 k P2 wV E E t Pw t t P1 P wS U w 0 0 A AA A AA A = P t 0 1 t 0 k P A P The probability of being observed in k varies linearly in time. This will clearly only work for short times, which is no surprise since we said for first-order P.T. b k t | b k 0 . So !! w k A represents the tangent to the relaxation behavior at t 0. !! w k A w P k A w t t 0 The problem is we don’t account for depletion of initial state. What long-time behavior do we expect? From an exact solution to the two-level problem, we saw that probability oscillates sinusoidally between the two states with a frequency given by the coupling: Cohen-Tannoudji, et al. p. 1344; Merzbacher, p. 510. MIT Department of Chemistry 5.74, Spring 2004: Introductory Quantum Mechanics II. Instructor: Prof. Andrei Tokmakoff
Background image of page 1

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

View Full DocumentRight Arrow Icon
p. 49 R / S: P t 1st order P.T. k P A P AA 0 1 0 !! : R ' 2 . V k A 2 = But we don’t have a two-state system. Rather, we are relaxing to a continuum. Fermi’s Golden Rule says we have a time-independent rate, !!
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

Page1 / 6

7 - MIT Department of Chemistry 5.74 Spring 2004...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online