PROBLEM 2. Find the eigenvalues of a Hermitian operator represented by the following matrix: 1 Â = i 0 -i 1
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- b) Prove that the following operators are Hermitian 1) Z 2) LxFor l = 2, determine the matrix representation of the following operators a) L dan L_ b) Lx, Ly, dan LzConsider the following operators on a Hilbert space V³ (C): 0-i 0 ABAR-G , Ly i 0-i , Liz 00 √2 0 i 0 LE √2 010 101 010 What are the corresponding eigenstates of L₂? 10 00 0 0 -1 What are the normalized eigenstates and eigenvalues of L₂ in the L₂ basis?
- Really stuck on homeworkFor a particle moving in one dimension, show that the operator ?̂?̂ is NOT Hermitian. Construct an operator which corresponds to this physical observable product and is Hermitian. ? and ? are position and momentumof the particle.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.