Consider the matrix representation of Lx, Ly and L₂ for the case l = 1 (see Matrix Representation of Operators class notes pp. 11-12). (a) Construct the matrix representation of L2 for l = 1. (b) What are the eigenvalues and corresponding eigenvectors of L²? (c) Are the eigenvectors of L2 the same as those of L₂? Explain. (d) Compute L² \x; +1), where [x;+1) is the eigenvector of La corresponding to eigenvalue +ħ.
Consider the matrix representation of Lx, Ly and L₂ for the case l = 1 (see Matrix Representation of Operators class notes pp. 11-12). (a) Construct the matrix representation of L2 for l = 1. (b) What are the eigenvalues and corresponding eigenvectors of L²? (c) Are the eigenvectors of L2 the same as those of L₂? Explain. (d) Compute L² \x; +1), where [x;+1) is the eigenvector of La corresponding to eigenvalue +ħ.
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![Consider the matrix representation of Lx, Ly and L₂ for the case l = 1 (see Matrix Representation of
Operators class notes pp. 11-12).
(a) Construct the matrix representation of L² for l = 1.
(b) What are the eigenvalues and corresponding eigenvectors of L²?
(c) Are the eigenvectors of L² the same as those of L₂? Explain.
(d) Compute L² |x; +1), where |x;+1) is the eigenvector of La corresponding to eigenvalue +ħ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18ff836d-3cc8-4a2b-b721-7f7a69fbe250%2Ffaf72a8c-7b84-43da-aa56-bbf5078f76bf%2F7rclq5q_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the matrix representation of Lx, Ly and L₂ for the case l = 1 (see Matrix Representation of
Operators class notes pp. 11-12).
(a) Construct the matrix representation of L² for l = 1.
(b) What are the eigenvalues and corresponding eigenvectors of L²?
(c) Are the eigenvectors of L² the same as those of L₂? Explain.
(d) Compute L² |x; +1), where |x;+1) is the eigenvector of La corresponding to eigenvalue +ħ.
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