This problem studies the classical and quantum harmonic oscillators. (a) First, we study the classical oscillator. Take the solution x = xo sin(wt), which assumes that the particle is at x 0 at t 0. Calculate P(x) by determining what fraction of the total time the particle will spend in an interval dx around x. In other words, use the relation P.(x)dx = dt/T, where T is the period of oscillation. (b) Plot the quantum harmonic oscillator eigenfunctions (squared) for n = 3, 10, 20, 150 and compare with the classical solution(s).

This problem studies the classical and quantum harmonic oscillators. (a) First, we study the classical oscillator. Take the solution x = xo sin(wt), which assumes that the particle is at x 0 at t 0. Calculate P(x) by determining what fraction of the total time the particle will spend in an interval dx around x. In other words, use the relation P.(x)dx = dt/T, where T is the period of oscillation. (b) Plot the quantum harmonic oscillator eigenfunctions (squared) for n = 3, 10, 20, 150 and compare with the classical solution(s).

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter6: Quantum Mechanics In One Dimension

Section: Chapter Questions

Problem 38P

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