Let it be the X coordinate Pauli's matrix:(adsbygoogle = window.adsbygoogle || []).push({});

\begin{array}{ccc}

0 & 1 \\

1 & 0 \end{array}

According to my calculations, it's eigenvectors would require that the spinor components to take the same value, but then, in order to have two orthogonal eigenvectors, we would need the complex components to be orthogonal when doing the dot product.

I choose the eigenvectors ψ_1 =[1, 1] and ψ_2 = [i, i]. Then the dot product must be

ψ_1 · ψ_2 = 1 · i + 1 · i = 0.

That means that orthogonal phases inside the same spinor component must be treated as orthogonal components. Is that true?

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# Eigenvalues for X’s Pauli's matrix

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