Question: Consider a three-dimensional ket space. If a certain set of ortho-normal kets?say, | 1 >, | 2 >, and | 1 > ? are used

Consider a three-dimensional ket space. If a certain set of ortho-normal kets?say, | 1 >, | 2 >, and | 1 > ? are used as the base kets, the operators A and B are represented by with a and b both real.

9, B =0 a A =0 - ib a a ib

a. Obviously A exhibits a degenerate spectrum. Does B also exhibit a degenerate spectrum?

b. Show that A and B commute.

c. Find a new set of ortho-normal kets which are simultaneous eigenkets of both A and B. Specify the eigenvalues of A and B for each of the three eigenkets. Does your specification of eigenvalues completely characterize eacheigen ket?

9, B =0 a A =0 - ib a a ib

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a The characteristic equation det BAI 0 leads to Xbxb 0 Hence Amb and Ab is a twofoid degenerate ... View full answer

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