QM: Corrections to the energy

[Niles]

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

We are looking at a quantum mechanical system, where there is a perturbation H', so H = H0 + H', where H0 is the unperturbed Hamiltonian.

The exact eigenenergies (i.e. the eigenenergies of H) are given by:


E = V_0(1-\epsilon) \quad \tex{and}\quad E = V_0(1-\epsilon^2).


So far so good. The eigenenergies of H0 (i.e. the unperturbed eigenenergies) are given by:


E = V_0 \quad \tex{and}\quad E = V_0.


The first order corrections to the eigenenergies of H0 are given by: E=0 and E=-\epsilon V_0.

Here my question: How do I generally know which correction "belongs" to which unperturbed energy?

My book is "Griffiths Intro to QM", so feel free to quote from there: The above example is exercise 6.9.

Thanks in advance.

Best regards,
Niles.

[Niles]

Ok, I answered this question myself. The energies are the same, so it doesn't matter which energy we add the constants to.