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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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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