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Transformation to a different base

  1. Sep 16, 2008 #1
    1. A transformation from base S to base T. The three combinations
    C(x)=(-1/sqrt(2))(C(+) - C(-)), C(y)=(-i/sqrt(2))(C(+) - C(-)) and C(z)=C(0)
    transform to C'(x), C'(y) and C'(z) just the way that x,y,z transform to x',y' and z'. You can check that this is so by using the transformation laws (see below).

    2. Relevant equations From the point of view of S the state Φ (can be +S, 0S and -S) is described by the three numbers:
    C(+)=〈+S ⎢ Φ〉, C(0)=〈0S ⎢ Φ〉and C(-)=〈-S ⎢ Φ〉.
    From the point of view of T the state Φis described by the three numbers:
    C'(+)=〈+T ⎢ Φ〉, C'(0)=〈0T ⎢ Φ〉and C'(-)=〈-T ⎢ Φ〉.
    Transformation laws 〈+T ⎢ +S〉= exp(+ib), 〈0T ⎢ 0S〉=1 and 〈-T ⎢ -S〉=exp(-ib), all other possible amplitudes are equal to zero.

    3. The attempt at a solution I tried the following: C'(x)=(-1/sqrt(2))(C'(+) - C'(-))
    with C'(+)=〈+T ⎢ Φ〉=〈+T ⎢ +S〉= exp(+ib) and C'(-)=〈-T ⎢ Φ〉=〈-T ⎢ +S〉=0.
    It follows: C'(x)=(-1/sqrt(2))(exp(+ib))

    Am I on the right track and if so what does the upper result tell me?

    Thanks in advance!
  2. jcsd
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