Let |0) and 1) be two orthonormal vectors in a Hilbert space, i.e., they satisfy (0|0) = 1, (1|1) = 1, (0|1) = 0. Consider the following linear combinations of the vectors [0) and [1): |ø) = |0) + i|1), |v) = (1 + i)|0) — [1). - Compute a) (p), b) |(p|v)|², c) |||4)||. Express the following in terms of the vectors [0) and [1): d) |ø) + iv), e) |p)|v), f) A|v), where A = 1) (0|— 2|0)(1|.
Let |0) and 1) be two orthonormal vectors in a Hilbert space, i.e., they satisfy (0|0) = 1, (1|1) = 1, (0|1) = 0. Consider the following linear combinations of the vectors [0) and [1): |ø) = |0) + i|1), |v) = (1 + i)|0) — [1). - Compute a) (p), b) |(p|v)|², c) |||4)||. Express the following in terms of the vectors [0) and [1): d) |ø) + iv), e) |p)|v), f) A|v), where A = 1) (0|— 2|0)(1|.
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Transcribed Image Text:Let |0) and 1) be two orthonormal vectors in a Hilbert space, i.e., they satisfy
(0|0) = 1,
(1/1) = 1, (0|1) = 0.
Consider the following linear combinations of the vectors [0) and 1)
|ø) = |0) + i|1), |v) = (1 + i)|0) − |1).
Compute a) (p), b) |[p|v)|², c) |||4)||.
Express the following in terms of the vectors
[0) and 1):
d) |ø) + iv), e) o)), f) Alv),
where A = 1) (0|-2|0) (1.
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