(iii) Show that the wave function of the particle in the potential well is NA X w.(x) = C sin n = 1,2,3, -.. %3D L (iv) By normalisation, determine the value of C. (v) Prove that the energy of the particle inside the potential well is quantised.
(iii) Show that the wave function of the particle in the potential well is NA X w.(x) = C sin n = 1,2,3, -.. %3D L (iv) By normalisation, determine the value of C. (v) Prove that the energy of the particle inside the potential well is quantised.
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...
Related questions
Question
Kindly answer no iii, iv & v
![1. The general solution for a particle in a one-dimensional infinite potential
well of width L is given as
y(x) = C sin kx + Dcos kx
where C, D and k are constants.
(i)
What are the boundary conditions at the walls of the well?
Show that the coefficient k in the above solutions is
(ii)
NT
k =
L
n = 1, 2,3, -..
(ii)
Show that the wave function of the particle in the potential well
is
пах
w„(x) = C sin|
L
n = 1,2,3, -..
(iv) By normalisation, determine the value of C.
(v)
Prove that the energy of the particle inside the potential well is
quantised.
[Hint: sin? 0 = (1+sin 20).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3cfe08d-f4fe-42d1-b9a5-8b47b58a0c4b%2F5d57705f-b107-4792-b5a8-46f823808ec0%2Flmw6zpg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. The general solution for a particle in a one-dimensional infinite potential
well of width L is given as
y(x) = C sin kx + Dcos kx
where C, D and k are constants.
(i)
What are the boundary conditions at the walls of the well?
Show that the coefficient k in the above solutions is
(ii)
NT
k =
L
n = 1, 2,3, -..
(ii)
Show that the wave function of the particle in the potential well
is
пах
w„(x) = C sin|
L
n = 1,2,3, -..
(iv) By normalisation, determine the value of C.
(v)
Prove that the energy of the particle inside the potential well is
quantised.
[Hint: sin? 0 = (1+sin 20).]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY