Problem 6.2. For a classical harmonic oscillator whose position and momentum are x and p define the complex amplitude a(t) = x(t) + (i/(mw))p(t) (6.38) (1/2) (a + a*) and p = -(imw/2)(a - a*). a and a* evolve accord- iwa*. Show that for a harmonic oscillator at thermal so that x = ing to a equilibrium - -iwa; à* (a²) = ((a*)²) = 0; (|a|²) = 2kBT/(mw²) Use it to show that (x(t)x(0)) = (kBT/mw²) cos(wt). (6.39)

Problem 6.2. For a classical harmonic oscillator whose position and momentum are x and p define the complex amplitude a(t) = x(t) + (i/(mw))p(t) (6.38) (1/2) (a + a) and p = -(imw/2)(a - a). a and a* evolve accord- iwa. Show that for a harmonic oscillator at thermal so that x = ing to a equilibrium - -iwa; à (a²) = ((a*)²) = 0; (|a|²) = 2kBT/(mw²) Use it to show that (x(t)x(0)) = (kBT/mw²) cos(wt). (6.39)

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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