Hey, I recently had an exam where the quantum state were on the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex] |\psi\rangle = \frac{1}{\sqrt{2}} ( |+\rangle + i |-\rangle )[/tex]

Here I formed the density operator for the pure state

[tex] \rho(t) = |\psi\rangle \langle \psi| = \frac{1}{2} ( |+\rangle + i |-\rangle )( \langle +| - i \langle -| ) = \frac{1}{2} ( |+\rangle \langle + | + |- \rangle \langle - | + i(|-\rangle \langle + | - |+\rangle \langle -|)). [/tex]

However in the solutions for the exam the complex i's were not there, i.e the solutions states that

[tex] \rho = \frac{1}{2} ( |+\rangle \langle + | + |- \rangle \langle - | + |-\rangle \langle +| - |+\rangle \langle - |).[/tex]

Have I missed something here or is the suggested solution erroneous? Is there a reason why a density operator expansion should not have complex coefficients?

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# Complex coefficents in density operator expansion?

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