# Notation regarding the dipole approximation

1. Apr 6, 2012

### Niles

1. The problem statement, all variables and given/known data
Hi

Whenever I read about the dipole approximation in QM, then the Hamiltonian is given as
$$\hat {V}_{\text{dipole}} = -\mathbf{d}\cdot \mathbf{E}$$
where E is the electric field and d the dipole operator. What I am wondering about is that d is an operator. Is it wrong to include the hat in the interaction? As in
$$\hat {V}_{\text{dipole}} = -\hat{\mathbf{d}}\cdot \mathbf{E}$$

This is probably a silly question, but it is something that has been on my mind for some time.

Best,
Niles.

2. Apr 6, 2012

### fzero

It's normal to be pedantic about putting hats on operators when students are just starting to learn about them. Later on in the course they can distinguish operators from context, so they might get left off by laziness. In the case of the dipole operator above, it's also likely that putting the hat might cause some readers to believe that it refers to a unit vector, so it's reasonable to leave it off.

3. Apr 20, 2012

### Niles

I see, thanks!