What are the corrections to the energy in a quantum mechanical system?

[Niles]

Homework Statement

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.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.