- #1

Lucas-

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- TL;DR Summary
- I don't understand why we cannot obtain perturbative correction to a specific eigenstate in the degenerated case (ie. |2s>)

Hello,

In the case of Stark effect for example, one may find the correction for the |1s> state easily by applying non degenerated perturbation theory. However in the degenerated case it's seems as though we can only treat the whole n=2 level for example and not individual eigen states. That, I don't understand as, in reality we could make 2s hydrogen atom and place them in an electric field. What would happen ? Why can't we get let's say the first order |2s> correction ?

When we do the usual setup, we find the common eigenkets in the degenerate subspace of the original hamiltonian and the perturbation and their associated eigen values.

We observe linear combination of eigenkets yet, they don't seem to depend on the field intensity, so this would mean that when I turn the perturbation off, If, let's say I started with a |2s> hydrogen I would keep the superposition ? Shouldn't it go back to |2s> ?

I'm a bit confuse and I would appreciate it if someone could enlighten me !

In the case of Stark effect for example, one may find the correction for the |1s> state easily by applying non degenerated perturbation theory. However in the degenerated case it's seems as though we can only treat the whole n=2 level for example and not individual eigen states. That, I don't understand as, in reality we could make 2s hydrogen atom and place them in an electric field. What would happen ? Why can't we get let's say the first order |2s> correction ?

When we do the usual setup, we find the common eigenkets in the degenerate subspace of the original hamiltonian and the perturbation and their associated eigen values.

We observe linear combination of eigenkets yet, they don't seem to depend on the field intensity, so this would mean that when I turn the perturbation off, If, let's say I started with a |2s> hydrogen I would keep the superposition ? Shouldn't it go back to |2s> ?

I'm a bit confuse and I would appreciate it if someone could enlighten me !