Let's suppose that we have an entangled state of two systems ##A## and ##B##:(adsbygoogle = window.adsbygoogle || []).push({});

$$

\frac{1}{2}\left(|\psi_1 \phi_1\rangle+|\psi_2 \phi_2\rangle \right)

$$

where ##|\psi \rangle## and ##|\phi \rangle## are energy eigenstates of ##A## and ##B## respectively. However the eigenstates##|\phi_1\rangle## and ##|\phi_2\rangle## are degenerate:

$$

\hat{H}_B|\phi_1\rangle=E|\phi_1\rangle

$$

$$

\hat{H}_B|\phi_2\rangle=E|\phi_2\rangle

$$

What will be the state of the system ##AB## after measuring the energy of ##B## and finding the value ##E##?

My guess is:

$$

\frac{\left(|\psi_1\rangle+|\psi_2 \rangle \right)}{\sqrt{2}} \frac{\left(|\phi_1\rangle+\phi_2\rangle \right)}{\sqrt{2}}

$$

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# I Measuring entangled state of degenerate eigenstates

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