# Commutators of Pauli Matrices

1. Aug 5, 2013

### unscientific

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

Express the product

where σy and σz are the other two Pauli matrices defined above.

2. Relevant equations

3. The attempt at a solution

I'm not sure if this is a trick question, because right away both exponentials combine to give 1, where the result is simply σx

2. Aug 5, 2013

### kevinferreira

That's the whole point of the exercise, to see that the exponentials do not combine to give 1. To do such a thing, you would have to pass $exp(i\alpha\sigma^z)$ to the other side of $\sigma^x$. But $\left[\sigma^z,\sigma^x\right]\neq0$ so that you can't simply commute them.

Hint: express the exponential as a series.

3. Aug 7, 2013

### unscientific

Ah, I see what you mean, as the sum is a matrix and not a number. Silly me.

Last edited: Aug 7, 2013