# QM Sakurai 1.9 - Problem at last step only!

1. Sep 21, 2008

### alienskin562

1. The problem statement, all variables and given/known data

2. Relevant equations
3. The attempt at a solution
Word 2007 Version
These are here in this attached PDF. You can see where I'm stuck - how do I solve for a and b?? It just so happens that my BA is in math :(

a and b are related non-algebraically, no?

2. Sep 21, 2008

### weejee

These two equations are actually redundant, as an eigenvector equation is supposed to be.

You can express 'b' in terms of 'a' or vice versa, and an additional constraint comes from the normalization condition |a|^2 + |b|^2 = 1.

3. Sep 21, 2008

### alienskin562

Hey thanks, I'm such a n00b. Cleared up now.

4. Sep 23, 2009

### Bill Foster

How about clearing it up for me?

5. Sep 23, 2009

### alienskin562

Its just this Bill - since the eigenvalue equaiton is redundant, you can go ahead and specify either a or b as long as the normalization condition is still satisfied.

So, since its a free parameter, you set a equal to the expected solution eigenket, a=cos beta

Then you solve for b.

6. Sep 23, 2009

### Bill Foster

If a = cos(β), then how do you get it into the final form given by Sakurai? Because his form has a = cos(β/2)

7. Sep 23, 2009

### alienskin562

I just forgot the /2 :p