# Doubt in this Lecture

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 $$n_zα+n_−β=α$$
http://www.lecture-notes.co.uk/suss...ments/lecture-4/spin-in-arbitrary-directions/

Paul Colby
Gold Member
There are two equations for ##\alpha## and ##\beta## given by the eigenvalue equation. This is the one for ##\alpha##. The other is for ##\beta##.

vanhees71
Gold Member
2021 Award
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?

bhobba
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 $$n_zα+n_−β=α$$

Paul Colby
Gold Member
##\sigma_n## times the vector ##(\alpha,\beta)## gives the same vector multiplied by 1. The equation follows from the top row of the matrix.

Muthumanimaran
ok, thank you, now I understand how it comes. Initially I misunderstood the Lecture. Its pretty straightforward.