Consider a Hilbert space {|1), |2), |3)}. An observable is represented in this space by an...

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Consider a Hilbert space {|1), |2), |3)}. An observable is represented in this space by an operator that reads, as a matrix, = = 0 0 100 0 0 1 The ordering of row and column indices is (1), (2), (3). a) Write the operator in projector notation (that is, using Dirac bras and kets, as discussed in class). b) What are the possible measurement results? Find the normalized and orthogonal quantum states that will yield these results upon measurement with 100% certainty. Write the states in Dirac notation 3 ||ai) = cij|j j=1 with i, j = 1, 2, 3 and coefficients c; that you are supposed to find and to write out. What are the degeneracies of the possible measurement results? c) Assume an incident state |4) = 2 (|1) + |3)). What are the probabilities for the measurement results? What is the average measurement result? What is the variance, (||4) = (| ( (V||))) of the measurement? d) What are the corresponding states after measurement? Give the states in Dirac notation in both the original basis and in the basis generated by . Consider a Hilbert space {|1), |2), |3)}. An observable is represented in this space by an operator that reads, as a matrix, = = 0 0 100 0 0 1 The ordering of row and column indices is (1), (2), (3). a) Write the operator in projector notation (that is, using Dirac bras and kets, as discussed in class). b) What are the possible measurement results? Find the normalized and orthogonal quantum states that will yield these results upon measurement with 100% certainty. Write the states in Dirac notation 3 ||ai) = cij|j j=1 with i, j = 1, 2, 3 and coefficients c; that you are supposed to find and to write out. What are the degeneracies of the possible measurement results? c) Assume an incident state |4) = 2 (|1) + |3)). What are the probabilities for the measurement results? What is the average measurement result? What is the variance, (||4) = (| ( (V||))) of the measurement? d) What are the corresponding states after measurement? Give the states in Dirac notation in both the original basis and in the basis generated by .