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Consider an infinite square-well potential of width a, but shifted so that the infinite potential barriers lie at x=-a/2 and x = a/2 (see left diagram below). The eigen-wavefunctions of this Hamiltonian have the general form: Vn(x) = Ancos(nπx/α) + Вsin(nлx/a). V(x) V(x) x=-a/2 x=0 x = a/2 x= -a/2 x=0 x = a/2 (a) Write down the normalized wavefunctions for the ground state (n = 1) and the first-excited state (n = 2). You can do so by solving the Schrodinger equation with the appropriate boundary conditions or by otherwise using what you know about the infinite square-well. (b) Write down the general expression for the eigen-energies E,,. (c) Now the width of the well is reduced by half. The barriers now lie at x = 0 and x= a/2, as shown in the right diagram above. Write down the general expression for the eigen-energies E.

Consider an infinite square-well potential of width a, but shifted so that the infinite potential barriers lie at x=-a/2 and x = a/2 (see left diagram below). The eigen-wavefunctions of this Hamiltonian have the general form: Vn(x) = Ancos(nπx/α) + Вsin(nлx/a). V(x) V(x) x=-a/2 x=0 x = a/2 x= -a/2 x=0 x = a/2 (a) Write down the normalized wavefunctions for the ground state (n = 1) and the first-excited state (n = 2). You can do so by solving the Schrodinger equation with the appropriate boundary conditions or by otherwise using what you know about the infinite square-well. (b) Write down the general expression for the eigen-energies E,,. (c) Now the width of the well is reduced by half. The barriers now lie at x = 0 and x= a/2, as shown in the right diagram above. Write down the general expression for the eigen-energies E.

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)...
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Consider an infinite square-well potential of width a, but shifted so that the infinite potential barriers lie at x=-a/2 and x = a/2 (see left diagram below). The eigen-wavefunctions of this Hamiltonian have the general form: Vn(x) = Ancos(nπx/α) + Вsin(nлx/a). V(x) V(x) x=-a/2 x=0 x = a/2 x= -a/2 x=0 x = a/2 (a) Write down the normalized wavefunctions for the ground state (n = 1) and the first-excited state (n = 2). You can do so by solving the Schrodinger equation with the appropriate boundary conditions or by otherwise using what you know about the infinite square-well. (b) Write down the general expression for the eigen-energies E,,. (c) Now the width of the well is reduced by half. The barriers now lie at x = 0 and x= a/2, as shown in the right diagram above. Write down the general expression for the eigen-energies E.
Transcribed Image Text:Consider an infinite square-well potential of width a, but shifted so that the infinite potential barriers lie at x=-a/2 and x = a/2 (see left diagram below). The eigen-wavefunctions of this Hamiltonian have the general form: Vn(x) = Ancos(nπx/α) + Вsin(nлx/a). V(x) V(x) x=-a/2 x=0 x = a/2 x= -a/2 x=0 x = a/2 (a) Write down the normalized wavefunctions for the ground state (n = 1) and the first-excited state (n = 2). You can do so by solving the Schrodinger equation with the appropriate boundary conditions or by otherwise using what you know about the infinite square-well. (b) Write down the general expression for the eigen-energies E,,. (c) Now the width of the well is reduced by half. The barriers now lie at x = 0 and x= a/2, as shown in the right diagram above. Write down the general expression for the eigen-energies E.
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