# I Doubt in this Lecture

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1. Jun 15, 2016

### Muthumanimaran

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/

2. Jun 15, 2016

### Paul Colby

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. Jun 15, 2016

### vanhees71

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?

4. Jun 15, 2016

### Muthumanimaran

I don't how that's lead to the expression $$n_zα+n_−β=α$$

5. Jun 15, 2016

### Paul Colby

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

6. Jun 15, 2016

### Muthumanimaran

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