# Writing Hamiltonian in the basis

1. Oct 19, 2014

### TeddyYeo

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

$H = \frac{2e^2}{\hbar^2 C} \hat{p^2} - \frac{\hbar}{2e} I_c cos\hat\theta$,
where $[\hat\theta , \hat{p}] = i \hbar$
How can we write the expression for the Hamiltonian in the basis $|\theta>$
2. Relevant equations

3. The attempt at a solution

I have already solved most part of the question and this is just one part of it that I am not sure how to convert into the basis form.
Is it that I just now need treat
$\hat{p}] = -i \hbar ∇ which is means that it is -i \hbar frac{\partial }{ \partial \theta}$
and put
$H = \frac{2e^2}{C} \frac{\partial^2}{\partial\theta^2} - \frac{\hbar}{2e} I_c cos\hat\theta$
then this is the final form??

2. Oct 24, 2014

### Greg Bernhardt

No. $\hat{p^2}=-i \hbar ∇(-i \hbar ∇) =-h^2 \Delta$. Use the Laplace operator written in spherical polar coordinates.