Quick question on notation of the Hamiltonian

[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 Schrödinger equation

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

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

Thanks in advance

 

[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 ($V$).

 

[rwooduk]

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 ($V$).

Great thanks for clearing this up!