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## Homework Statement

What is the result of operating on the state |+> with the operator Sx?

here, |+> denotes the eigenstate of Sz with eigenvalue 1/2. I am working in units where h-bar is 1 (for simplicity, and because I don't know how to type it)

## Homework Equations

[tex]S_i = \frac{1}{2} σ_i [/tex]

## The Attempt at a Solution

My understanding of the physics of the problem is that after measurement the system will be in state where the x component of its spin is certain, as [Sx,Sz] != 0 this means it will be in some superposition of the states |+> and |-> My intuition tells me that the probability for the particle to be found in either state should be equal.

However, operating with the matrix representation of Sx :[tex]\frac{1}{2}

\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right)

[/tex]

on |+> just gives (1/2)|->

What am i doing wrong?