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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
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 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).]
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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