nian is given by H = p2/2m + m[omega]2x2/2. a) Determine the Ehrenfest equations of motion for and . b) Solve these equations for the initial conditions = x0, = p0, where x0 and p0 are real constants. Better formatted version of the question attached.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question

According to Ehrenfest's theorem, the time evolution of an expectation value <A>(t) follows the Ehrenfest equations of motion (d/dt)<A>(t) = (i/[hbar])<[H,A]>(t).

For the harmonic oscillator, the Hamiltonian is given by H = p2/2m + m[omega]2x2/2.

a) Determine the Ehrenfest equations of motion for <x> and <p>.

b) Solve these equations for the initial conditions <x> = x0, <p> = p0, where x0 and p0 are real constants.

Better formatted version of the question attached. 

According to Ehrenfest's theorem, the time evolution of an expectation value (Ä)(t) follows
d
the Ehrenfest equations of motion (Â)(t) = (IĤ, Ã])(t).
For the harmonic oscillator, the Hamiltonian is given by Ĥ = /2m + mw?â²/2.
(a) Determine the Ehrenfest equations of motion for (î) and (p).
(b) Solve these equations for the initial conditions (î) = xo, (p) = Po, where xo and po are
real constants.
Transcribed Image Text:According to Ehrenfest's theorem, the time evolution of an expectation value (Ä)(t) follows d the Ehrenfest equations of motion (Â)(t) = (IĤ, Ã])(t). For the harmonic oscillator, the Hamiltonian is given by Ĥ = /2m + mw?â²/2. (a) Determine the Ehrenfest equations of motion for (î) and (p). (b) Solve these equations for the initial conditions (î) = xo, (p) = Po, where xo and po are real constants.
Expert Solution
steps

Step by step

Solved in 5 steps with 5 images

Blurred answer
Knowledge Booster
Degenerate Perturbation theory
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON