# 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.

Best regards,
Niles.

Last edited:
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#### Niles

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

"QM: Corrections to the energy"

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