So I understand what a hermitian operator is and how if A and B are hermitian operators, then the product of AB is not necessarily Hermitian since(adsbygoogle = window.adsbygoogle || []).push({});

*Note here + is dagger

(AB)+=B+A+=BA

I also recognize that (AB-BA) is not Hermitian since (AB-BA)+=B+A+-A+B+

In addition, I know that any real number a is a Hermitian operator since <Psi l|a Psi n>=<aPsi l|Psi n>

Now here comes my questions.

Where A and B are both hermitian operators,

1)how do we know if something like i(AB-BA) is a hermitian operator where i is an imaginary number? How do I show that this is not a hermitian operator because I am pretty sure it is not?

2) and how would I show that (AB+BA/2) is Hermitian because I feel like it should be, but I dont know how to interchange the 2 with the A and B operators?

And if operator A corresponds to observable A, and operator B corresponds to observable B, what is a "good" (i.e.Hermitian) operator that corresponds to the physically observable product AB?

When I am dealing with two operators, I dont think I am confused on how to work with them, but when dealing with 3 I get a little iffy. Peace and love.

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# Hermitian Operators and Imaginary Numbers

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