Let us define [tex]\hat{R} = |\psi_m\rangle \langle \psi_n|[/tex] where [tex]\psi_n[/tex] denotes the [tex]n[/tex]th eigenstate of some Hermitian operator. When is [tex]\hat{R}[/tex] Hermitian?(adsbygoogle = window.adsbygoogle || []).push({});

Solution?

Well, let us just call |psi_m> = |m> and |psi_n> = |n>. Now, we need

|m><n| = |n><m|

If we left multiply by <m| then we find that

<n| = 0

By symmetry, if we left multiply by <n| we find that

<m| = 0

But, clearly, by inspection, we find that R is Hermitian if |m> = |n>. Are these all the solutions?

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# Hermitian Operator Question

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