- #1
center o bass
- 560
- 2
Hey, I recently had an exam where the quantum state were on the form
[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?
[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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