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The wavefunction for a spin 1/2 particle is a spinor field of the form [tex]\psi(\mathbf{x},t)=\left(

\begin{array}{cc}

\psi_{+}(\mathbf{x},t)\\

\psi_{-}(\mathbf{x},t)

\end{array}

\right).[/tex]

[itex]\psi_{+}(\mathbf{x},t)[/itex] is the amplitude that the particle is both spin up and located at position x at time t. How can I calculate the amplitude that the particle is just spin up, without any regards for its position? Would it be something like

[tex]\int \psi_{+}(\mathbf{x,t})d^3 \mathbf{x}?[/tex]

\begin{array}{cc}

\psi_{+}(\mathbf{x},t)\\

\psi_{-}(\mathbf{x},t)

\end{array}

\right).[/tex]

[itex]\psi_{+}(\mathbf{x},t)[/itex] is the amplitude that the particle is both spin up and located at position x at time t. How can I calculate the amplitude that the particle is just spin up, without any regards for its position? Would it be something like

[tex]\int \psi_{+}(\mathbf{x,t})d^3 \mathbf{x}?[/tex]

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