Change of Basis: Converting Wavefunction from S_z to S_x

[Norman]

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

 

[Norman]

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

 

[quantumdude]

You've basically got it. To convert from S_z to S_x, you rotate the state vector p/2 rad about the y-axis.

 

[ModusPwnd]

You've basically got it. To convert from S_z to S_x, you rotate the state vector p/2 rad about the y-axis.

Hi, I know this is old. I am 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?