# Questions tagged [perturbation-theory]

Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.

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### Perturbation theory for an asymmetric top

I am working through Prof. Littlejohn's notes on perturbation theory, and I'm trying exercise number 2, which asks to analyze an asymmetric top (exact problem statement in the notes). I'm confused ...
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### "Good" eigenstates for hydrogen atom in first excited state in an electric field

Consider a hydrogen atom in the first excited state that is being kept in an external electric field of strength $\lambda E_{ext}\mathbf {\hat{k}}$ . This electric field causes the splitting of the ...
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### Why does degenerate perturbation theory work? [duplicate]

As is well-known, the first-order correction to the $n$th unperturbed eigenstates is given by $$|\psi^n_1 \rangle = \sum_m \frac{\langle m| H_1 |n \rangle}{\varepsilon_n - \varepsilon_m},$$ where I ...
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### Vector perturbations in an expanding universe

Why vector perturbations in an expanding universe decay while the scalar and tensor perturbations don't?
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### 2D Q.H.O and degenerate time independent Perturbation theory

In the case when we consider the 2D quantum harmonic oscillator, we also consider an additional disturbance operator of the form $W=Kxy$. If we consider the eigenvalue $E_1$, where $n=1$, these ...
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### An instance of the equality of the transition rates $W_{i\to f}$ and $W_{f\to i}$ from Fermi's Golden rule

Fermi's Golden Rule tells that for a perturbing Hamiltonian $\hat{V}$ that couples initial state $\left| i \right\rangle$ to final state $\left| f \right\rangle$, the transition probability per unit ...