2D subspace of a Hilbert space

  • #1
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Homework Statement


Have to read a paper and somewhere along the line it claims that for any distinct ## \ket{\phi_{0}}## and ##\ket{\phi_{1}}## we can choose a basis s.t. ## \ket{\phi_{0}}= \cos\frac{\theta}{2}\ket{0} + \sin\frac{\theta}{2}\ket{1}, \hspace{0.5cm} \ket{\phi_{1}}= \cos\frac{\theta}{2}\ket{0} - \sin\frac{\theta}{2}\ket{1}##

where $$\theta$$ is between 0 and pi/2. Why pi/2? doesn't the upper bound have to be pi so that the inner product of the two can be anywhere between 1 and -1 (rather than between 1 and 0)

Homework Equations




The Attempt at a Solution

 

Answers and Replies

  • #2
Orodruin
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The values of the angle > pi/2 is just a reordering and rephasing of the values < pi/2.
 

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