# Ground state energy

I am looking at a diatomic molecule where the Hamiltonian is given as

H = l²/2I + F*d*cos theta

where d is the dipole moment. The term F*d*cos theta is small. I write the energy of ground state as

E_0 = \hbar*l*(l+1)/ 2I

Than I have to determine how much the ground-state energy changes as a result of interaction with the field. I have two questions:

1. Is the ground state energy correct - it should not be <psi_0|H|psi_0)?

2. How to proceed using first-order perturbation theory

Gokul43201
Staff Emeritus
Gold Member
1. Write down the eigenfunctions of the unperturbed hamiltonian, $H _0 = L^2/2I$ (recall from the hydrogen atom), and it's eigenvalues (already written above).

2. From the eigenfunctions, $\phi _n ^{(0)}$ and the eigenvalues, $E_n^{(0)}$, what expression gives you the first order energy shift due to the perturbing hamiltonian, $H _1$?

so the change will be given as
E_1 = <psi_0|V|psi_0>
where V is the small term?

dextercioby
Homework Helper
That's right, that's the first order correction to the ground state energy.

Thanks could there be a situation where an electronic excited state could be "ground state" for a molecule - having lower energy than a none excited state?

dextercioby