# Quick question on notation of the Hamiltonian

1. Dec 23, 2014

### rwooduk

for a degnerate system it's in my notes that you can write:

$$H^{(0)}\Psi _{1}=E_{0}\Psi _{1}$$
$$H^{(0)}\Psi _{2}=E_{0}\Psi _{2}$$

and (not related) we write the general Schrodinger equation

$$H_{0}\Psi + V\Psi = E\Psi$$

Please could someone tell me what both the upper and lower zeros on the H mean?

2. Dec 23, 2014

### ShayanJ

For the "upper zeroes", it seems to me its in the context of degenerate perturbation theory. Then that zero means its the unperturbed Hamiltonian.
For the "lower zero", the full Hamiltonian is written as the free Hamiltonian($H_0$) plus a potential(interaction) part ($V$).

3. Dec 24, 2014

### rwooduk

Great thanks for clearing this up!