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Homework Help: Does |z> = |+z> + |-z> ?

  1. Sep 30, 2006 #1
    does |z> = |+z> + |-z> ?
  2. jcsd
  3. Sep 30, 2006 #2
    No, |+z> + |-z> = |z> - |z> = 0.
  4. Sep 30, 2006 #3
    umm..., no.
  5. Sep 30, 2006 #4
    What is [itex] | z \rangle [/itex]?
    Last edited: Sep 30, 2006
  6. Sep 30, 2006 #5
    In quantum mechanics, |z> is a state vector read at "ket z".

    It describes the state a particle is in.
  7. Sep 30, 2006 #6
    Yeah, but if [itex] | z_+ \rangle, | z_- \rangle [/itex] are basekets of the Hilbert space you consider, your equation would be a definition of [itex] | z \rangle[/itex]
  8. Sep 30, 2006 #7
    is it a valid/correct definition?

    I'm in an intro quantum class and I need to calculate:

    so far, we have just been calculating things like: <+or-phi|+or-psi>

    Now we are asked to calculate things like:


    Which i read as that is the amplitude of something in either the +x or -x state being in the -z state.
  9. Sep 30, 2006 #8
    No since |z>=(1,0) in the z basis and |-z>= (0,1) in the z basis you could a. never get a scalar under addition and you could not get an answer of the zero vector since these vectors are linearly independent and form a complete basis. For your previous post you need to calculate what |-z> is in the x basis or what |x> is in the z basis to compute the inner product. Griffiths QM or Liboff are good sources for this. As is Nielsen and Chuang

    Hope that helps
  10. Sep 30, 2006 #9
    |z> is not equal to |+z>

    I thought |+z>=(1,0)
  11. Sep 30, 2006 #10
    For a QM-Interpretation you have to normalize the statevector, so that
    [itex] \langle z | z \rangle = 1 [/itex]. If [itex] \langle z_+ | z_+ \rangle = 1 [/itex] and [itex] \langle z_- | z_- \rangle = 1[/itex]-, this not the case here.

    I wouldn't say "amplitude" but "probability": [itex] |\langle -z | x \rangle|^2 [/itex] is the probability to measure "z-spin-down" on a particle of which you know it is in state "x-spin-up".
  12. Sep 30, 2006 #11
    <-z|-z> = 1

    <-z|-z> means what is the "probability" amplitude that a particle in state |-z> will be in state |-z>
  13. Sep 30, 2006 #12
    Yeah, I just wanted to say that your probability of finding z in state z from the equation above would be [itex] 2^2=4 [/itex], so you have to normalize.
  14. Sep 30, 2006 #13
    you dont have to write the plus explicity. |z>=|+z>=(1,0) which is not equal to -|-z>=(0,-1). The negatives are part of the nomenclature and do not have algebraic signifigance.
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