Homework Help is Here – Start Your Trial Now!
Science
Physics
The most general form of the Schrodinger equation is: a(r, t) Ət ħ² -V²V(r, t) + V(r, t)(r, t), 2m where V(r, t) is the potential energy. We consider a free particle moving in the x-dimension. iħ 1) Show that the Hamiltonian operator can be written as

The most general form of the Schrodinger equation is: a(r, t) Ət ħ² -V²V(r, t) + V(r, t)(r, t), 2m where V(r, t) is the potential energy. We consider a free particle moving in the x-dimension. iħ 1) Show that the Hamiltonian operator can be written as

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)...
See similar textbooks
icon
Related questions
Question

slove part 2

The most general form of the Schrodinger equation is: a(r, t) Ət ħ² -V²v(r, t) + V(r, t)V(F, t), 2m where V(r, t) is the potential energy. We consider a free particle moving in the x-dimension. iħ 1) Show that the Hamiltonian operator can be written as ħ² d² 2m dx²¹ Ĥ = - H and verify that V₁(x) = eikx, V₂(x) = cos(kx) and V3(x) = sin(kx) are stationary solutions of the corresponding Schrodinger equation (write it ex- plicitely). 2) The momentum operator in one dimension is pa = -ih Calculate ÎxV₁(x), ÎxV₂(x) and pV3(x). Are V₁(x), V₂(x) or V3(x) eigenfunctions of the momentum operator? Why? What are the corresponding eigenvalues?
Transcribed Image Text:The most general form of the Schrodinger equation is: a(r, t) Ət ħ² -V²v(r, t) + V(r, t)V(F, t), 2m where V(r, t) is the potential energy. We consider a free particle moving in the x-dimension. iħ 1) Show that the Hamiltonian operator can be written as ħ² d² 2m dx²¹ Ĥ = - H and verify that V₁(x) = eikx, V₂(x) = cos(kx) and V3(x) = sin(kx) are stationary solutions of the corresponding Schrodinger equation (write it ex- plicitely). 2) The momentum operator in one dimension is pa = -ih Calculate ÎxV₁(x), ÎxV₂(x) and pV3(x). Are V₁(x), V₂(x) or V3(x) eigenfunctions of the momentum operator? Why? What are the corresponding eigenvalues?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Parity
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.
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
SEE MORE TEXTBOOKS