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Showing that general operator equations are hermitian

  • Thread starter UCLphysics
  • Start date
1. The problem statement, all variables and given/known data

a)For a general operator A, show that and i(A-A+) are hermitian?

b) If operators A and B are hermitian, show that the operator (A+B)^n is Hermitian.

2. Relevant equations

3. The attempt at a solution

The first part I did,



The second part I used binomial expansion (induction) but I was told they do not commute so this cannot be done?

Is my answer to the first part correct and what route should I take for the second? Thanks
First part looks about right.

For the second part, do you really need to multiply things out? After all, if A and B are Hermitian then A+B is also Hermitian...


Science Advisor
Homework Helper
Insights Author
The problems seems to have no connection with <Advanced Physics> and neither with mathematics, since it's not mathematically (i.e. in agreement with mathematics) formulated and not even semantically.


Science Advisor
Homework Helper
Insights Author
For example, the mathematical problem for point a) should have been

"Let A be a densly defined linear operator on a complex separable Hilbert space [itex] \mathcal{H}[/itex].

Prove that if [itex] D(A)\cap D\left(A^{\dagger}\right) [/itex] is dense everywhere in [itex] \mathcal{H} [/itex],

then the operator [itex] i\left(A-A^{\dagger}\right) [/itex] is symmetric.

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