Is the product rule on operators different from traditional calculus?

[Abigale]

Hey Guys,

I regard two operators \Psi , \Phi, that don't commute.

Does the product-rule, looks like that?

$$\nabla (\Phi \Psi)

= \Psi (\nabla \Phi)

+\Phi (\nabla \Psi)

$$

THX

 

[maajdl]

How do you define the different items in this equation?
For example if Ψ = ∇, how do you define ∇Ψ ?
And in general?

 

[Bill_K]

Does the product-rule, looks like that?
$$\nabla (\Phi \Psi) = \Psi (\nabla \Phi) +\Phi (\nabla \Psi) $$

You need to keep the original order:

$$\nabla (\Phi \Psi) = (\nabla \Phi) \Psi+\Phi (\nabla \Psi) $$