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I Doubt in this Lecture

  1. Jun 15, 2016 #1
    I am currently reading Prof.Leonard Susskind's Lecture on Quantum Mechanics. In the Chapter: Spin in the arbitrary directions, in the subdivision Eigenstates
    In case $$\lambda=1$$
    Prof states that measuring spin in arbitrary +n state gives me +1 as eigenvalue, what I don't understand is the next expression $$n_zα+n_−β=α$$
    I have no idea how this expression comes here, please help me. The link to the lecture is given below:
    http://www.lecture-notes.co.uk/suss...ments/lecture-4/spin-in-arbitrary-directions/
     
  2. jcsd
  3. Jun 15, 2016 #2

    Paul Colby

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    There are two equations for ##\alpha## and ##\beta## given by the eigenvalue equation. This is the one for ##\alpha##. The other is for ##\beta##.
     
  4. Jun 15, 2016 #3

    vanhees71

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    I don't see any obvious mistakes (I've not followed everything thoroughly). All that Suskind in fact does is to diagonalize the matrix ##\vec{n} \cdot \vec{\sigma}##. Where's your specific problem?
     
  5. Jun 15, 2016 #4
    I don't how that's lead to the expression $$n_zα+n_−β=α$$
     
  6. Jun 15, 2016 #5

    Paul Colby

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    ##\sigma_n## times the vector ##(\alpha,\beta)## gives the same vector multiplied by 1. The equation follows from the top row of the matrix.
     
  7. Jun 15, 2016 #6
    ok, thank you, now I understand how it comes. Initially I misunderstood the Lecture. Its pretty straightforward.
     
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