Doubt in this Lecture

  • #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/
 

Answers and Replies

  • #2
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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##.
 
  • #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?
 
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  • #4
There are two equations for ##\alpha## and ##\beta## given by the eigenvalue equation. This is the one for ##\alpha##. The other is for ##\beta##.
I don't how that's lead to the expression $$n_zα+n_−β=α$$
 
  • #5
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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.
 
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  • #6
ok, thank you, now I understand how it comes. Initially I misunderstood the Lecture. Its pretty straightforward.
 

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