b 2 Given the results of problem 5 you will not be able to completely determine

# B 2 given the results of problem 5 you will not be

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b # . (2) Given the results of problem 5, you will not be able to completely determine the complex numbers a and b . Therefore, you may want to 2
arbitrarily take a to be real and positive, and to take b to be another real positive number times a phase factor e to be determined. 7. (10 pts) In the following c, d, e . . . are arbitrary complex numbers, | A i , | B i . . . are arbitrary kets, h E | , h F | . . . are arbitrary bras, and ˆ O, ˆ P . . . are ar- bitrary operators. State whether each of the following expressions is a number, a ket, a bra, an operator, or none of the above, and briefly justify your answer. (a) | A ih E | (b) | A ih E | c | B i (c) | A ih E | c | B ih F | (d) | A ih E | c | B ih F | d h G | (e) h E | ˆ O | A i (f) h E | ˆ O ˆ P | A i (g) h E | ˆ O | A i ˆ P (h) ˆ P | A ih E | (i) h E | ˆ O ˆ P 3

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• Fall '15
• mechanics, Work, Hilbert space, spinors, Townsend problem, Townsend Section

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