Where Does the Double Hat in the Hamiltonian Raising Operator Come From?

[Chronos000]

Homework Statement

I'm given the line: (the coding stopped responding for the "hats")

$$\hat{}H$$($$\hat{}a$$|n>) = (doublehat a) H(hat) |n> + [Hhat,ahat]|n>

I'm assuming Hhat= hbar *w ( aa* + 1/2)

so I don't know what they are doing. where does the double hat come from. where does any of it come from basically?

 

[MathematicalPhysicist]

The hat just comes to differentiate between a hermitian operator and its eigenvalue.
I am not sure myself what the the doublhat means in your case.

Anyway this equation is from the commutator relation:
$$[H,a]= Ha - aH$$

 

[Chronos000]

but this expression includes the commutation [H,a].