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3. Let's have another swing at the one-dimensional harmonic oscillator. Suppose that the oscillator is prepared in one of the eigenstates of the Hamiltonian, [y) = |n), where n = {0, 1, 2,...}. (a) What is the variance in the energy of the system in the state |)? Hint: Recall that the Hamiltonian operator is an observable that corresponds to the total energy of the system. (b) Express the position operator â and the momentum operator p in terms of the ladder operators â and â¹.

3. Let's have another swing at the one-dimensional harmonic oscillator. Suppose that the oscillator is prepared in one of the eigenstates of the Hamiltonian, [y) = |n), where n = {0, 1, 2,...}. (a) What is the variance in the energy of the system in the state |)? Hint: Recall that the Hamiltonian operator is an observable that corresponds to the total energy of the system. (b) Express the position operator â and the momentum operator p in terms of the ladder operators â and â¹.

College Physics
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)...
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3. Let's have another swing at the one-dimensional harmonic oscillator. Suppose that the oscillator is prepared in one of the eigenstates of the Hamiltonian, [y) = |n), where n = {0, 1, 2,...}. (a) What is the variance in the energy of the system in the state |)? Hint: Recall that the Hamiltonian operator is an observable that corresponds to the total energy of the system. (b) Express the position operator â and the momentum operator p in terms of the ladder operators â and â¹.
Transcribed Image Text:3. Let's have another swing at the one-dimensional harmonic oscillator. Suppose that the oscillator is prepared in one of the eigenstates of the Hamiltonian, [y) = |n), where n = {0, 1, 2,...}. (a) What is the variance in the energy of the system in the state |)? Hint: Recall that the Hamiltonian operator is an observable that corresponds to the total energy of the system. (b) Express the position operator â and the momentum operator p in terms of the ladder operators â and â¹.
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