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 NT X w„(x) = C sin| 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).] 2
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 NT X w„(x) = C sin| 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).] 2
Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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Kindly answer no i, ii & iii
![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%2F65e5efd0-4d30-4645-b83a-47f8817c8095%2Fscn272f_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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