# Quantum Mechanics, changing basis

1. Oct 13, 2012

### danJm

1. The problem statement, all variables and given/known data
Determine the column vectors representing the states |+x> and |-x> using the states |+y> and |-y> as a basis.

2. Relevant equations
?

3. The attempt at a solution
The hint my prof gave us was that since |+x> = 1/√2|+z> + 1/√2|-z> we can eliminate the states |+z> and |-z> in favor of |+y> and |-y>

I'm just lost I guess, i'm not sure how to eliminate the z states in favor of y. Any further hint or suggestion would be much appreciated.

2. Oct 13, 2012

### vela

Staff Emeritus
Think about where |+x> = 1/√2|+z> + 1/√2|-z> came from, and what exactly you mean by |+x>, |-x>, |+y>, |-y>, |+z>, and |-z>.

I assume you're talking about spin 1/2. You never really said.

3. Oct 13, 2012

### danJm

yes, spin 1/2 particles.

The book we're using is Townsend, A Modern Approach to QM. The book starts with spin 1/2 particles and examination of the Stern-Gerlach experiment.

When it's talking about finding the constants (e.g. 1/√2) it says one solution is to choose c+ and c- to be real, namely c+=1/√2 and c-=1/√2, the more general solution for c+ and c- may be written
c+=ei$\delta+$/√2 and
c-=ei$\delta+$/√2

where $\delta+$ and $\delta-$ are real phases that allow for the possibility that c+ and c- are complex.

That said, can i just name |+x> in the y basis similarly to it was in the z basis?
It seems kinda vague to me.

4. Oct 13, 2012

### vela

Staff Emeritus
I'm not sure what you mean by "just name |+x> in the y basis similarly to it was in the z basis". There are precise definitions to the basis vectors. Do you know what they are?

5. Oct 13, 2012

### danJm

no, apparently i do not.

6. Oct 13, 2012

### vela

Staff Emeritus
What's their relation to the spin operators Sx, Sy, and Sz?