(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...
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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).]
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