For l = 2, determine the matrix representation of the following operators a) L dan L_ b) Lx, Ly, dan Lz
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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.Consider the following operator imp Â= and the following functions that are both eigenfunctions of this operator. mm (0) = e² ‚ (ø) = (a) Show that a linear combination of these functions d² dø² is also an eigenfunction of the operator. (b) What is the eigenvalue? -m imp c₁e¹m + c₂e² -imp -imp = e