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Homework Help: QM Sakurai 1.9 - Problem at last step only!

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data

    http://www.ocf.berkeley.edu/~yayhdapu/postings/sak19.gif [Broken]

    2. Relevant equations
    3. The attempt at a solution
    http://www.ocf.berkeley.edu/~yayhdapu/postings/sakurai1.9.pdf" [Broken]
    http://www.ocf.berkeley.edu/~yayhdapu/postings/sakurai1.9.docx" [Broken]
    These are here in this attached PDF. You can see where I'm stuck - how do I solve for a and b?? It just so happens that my BA is in math :(

    http://www.ocf.berkeley.edu/~yayhdapu/postings/sak19_2.gif [Broken]

    a and b are related non-algebraically, no?
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Sep 21, 2008 #2
    These two equations are actually redundant, as an eigenvector equation is supposed to be.

    You can express 'b' in terms of 'a' or vice versa, and an additional constraint comes from the normalization condition |a|^2 + |b|^2 = 1.
  4. Sep 21, 2008 #3
    Hey thanks, I'm such a n00b. Cleared up now.
  5. Sep 23, 2009 #4
    How about clearing it up for me?
  6. Sep 23, 2009 #5
    Its just this Bill - since the eigenvalue equaiton is redundant, you can go ahead and specify either a or b as long as the normalization condition is still satisfied.

    So, since its a free parameter, you set a equal to the expected solution eigenket, a=cos beta

    Then you solve for b.
  7. Sep 23, 2009 #6
    If a = cos(β), then how do you get it into the final form given by Sakurai? Because his form has a = cos(β/2)
  8. Sep 23, 2009 #7
    I just forgot the /2 :p
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