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Quantum Mechanics, changing basis

  1. Oct 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the column vectors representing the states |+x> and |-x> using the states |+y> and |-y> as a basis.


    2. Relevant equations
    ?


    3. The attempt at a solution
    The hint my prof gave us was that since |+x> = 1/√2|+z> + 1/√2|-z> we can eliminate the states |+z> and |-z> in favor of |+y> and |-y>

    I'm just lost I guess, i'm not sure how to eliminate the z states in favor of y. Any further hint or suggestion would be much appreciated.
     
  2. jcsd
  3. Oct 13, 2012 #2

    vela

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    Think about where |+x> = 1/√2|+z> + 1/√2|-z> came from, and what exactly you mean by |+x>, |-x>, |+y>, |-y>, |+z>, and |-z>.

    I assume you're talking about spin 1/2. You never really said.
     
  4. Oct 13, 2012 #3
    yes, spin 1/2 particles.

    The book we're using is Townsend, A Modern Approach to QM. The book starts with spin 1/2 particles and examination of the Stern-Gerlach experiment.

    When it's talking about finding the constants (e.g. 1/√2) it says one solution is to choose c+ and c- to be real, namely c+=1/√2 and c-=1/√2, the more general solution for c+ and c- may be written
    c+=ei[itex]\delta+[/itex]/√2 and
    c-=ei[itex]\delta+[/itex]/√2

    where [itex]\delta+[/itex] and [itex]\delta-[/itex] are real phases that allow for the possibility that c+ and c- are complex.

    That said, can i just name |+x> in the y basis similarly to it was in the z basis?
    It seems kinda vague to me.
     
  5. Oct 13, 2012 #4

    vela

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    I'm not sure what you mean by "just name |+x> in the y basis similarly to it was in the z basis". There are precise definitions to the basis vectors. Do you know what they are?
     
  6. Oct 13, 2012 #5
    no, apparently i do not.
     
  7. Oct 13, 2012 #6

    vela

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    What's their relation to the spin operators Sx, Sy, and Sz?
     
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