# Change of basis

1. ### Norman

919
Hello all,

I need some help...
If I know the form of a wavefunction in the $S_z$ basis, say it is spin up, how do I convert that to a wavefunction expressed in the $S_x$ basis? Is there a very simple way to do this?
Thanks

2. ### Norman

919
Anyone???
Do I just rotate the spinor using a rotation operator?
Help?

3. ### Tom Mattson

5,526
Staff Emeritus
You've basically got it. To convert from Sz to Sx, you rotate the state vector p/2 rad about the y-axis.

4. ### ModusPwnd

Hi, I know this is old. Im sorry, but I have some confusion about this.

I wonder, shouldn't the new state vector be a superposition of +x and -x? If I apply the rotation operator to my z state I get a pure state.

Where has my thinking gone wrong?

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