Change of basis

Norman

Hello all,

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

Norman

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

Tom Mattson

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

Quote by Tom Mattson

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. 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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Norman Blog Entries: 12	Change of basis Tweet Hello all, I need some help... If I know the form of a wavefunction in the [itex] S_z [/itex] basis, say it is spin up, how do I convert that to a wavefunction expressed in the [itex] S_x [/itex] basis? Is there a very simple way to do this? Thanks

Tom Mattson Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus	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.