# 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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### Selection rule in three dimensional harmonic oscillator in representation $(n,l,m)$

I'm now doing exercises about selection rule for transition probability of first order perturbation. But in the one where a periodic perturbation Axcos(ωt) add to a three dimensional harmonic ...
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### Degeneracy in time-independent perturbation theory

I have a problem understanding the reasoning of my professor in Quantum Mechanics. The topic is time-independent perturbation theory. Let $H = H_0 + \lambda H_1$ be a perturbed Hamilton-Operator and ...
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### Possible decays of a scalar particle, Feynman diagrams and calculation of branching ratio - Explenation of solution required

Consider the Lagrangian describing two Dirac fields of masses $m_1$ and $m_2$ and a scalar neutral field of mass $M$, which in addition to the free terms contains the following interaction term \begin{...
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### How can I count diagrams (in this scalar QED example) at a particular order without drawing all the Feynman diagrams?

Here's a 3-loop diagram for light-by-light scattering in scalar QED (from Schwartz textbook question 9.2): The question 9.2 asks approximately how many other diagrams contribute at the same order in ...
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### Solutions for nonrelativistic-matter perturbations

I'm studying the nonrelativistic-matter perturbations if the expansion of the Universe is driven by a combination of components. I'm currently Following this document (The growth of density ...
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### Derivation of ODE for $c_n(t)$ in Time-dependent Perturbation Theory [closed]

I'm going through the notes on Time-dependent perturbation theory from MIT OCW and want to make sure I understand how we're going from the first equality to the second in the picture attached below: ...
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### Is there an error bound for perturbation theory?

It is usually said that perturbation theory is valid when the perturbation is much smaller than the spacing between energy levels. However, I was thinking whether there exists an rigorous error bound. ...
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### Scale dependent density growth in sub-horizon scales

In standard cosmology, we use $$\ddot{\delta} + 2 H \dot{\delta} - 4 \pi G_N \rho \delta=0 \tag{1}$$ to study the structure growth in sub-horizon scales. However, at the ...
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### Transformation under coordinate transformation of scalar perurbation of FLRW metric

For the past few days I've been studying perturbation in cosmology. More specifically I am now busy with chapter 6 in Dodelson's Modern cosmology. In this book the perturbed FLRW metric which only ...
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### Ratio of scale factors during matter-radiation equality

For the past few days I've been studying cosmology using Dodelson's book. I am now busy with chapter 8 and was making some exercises. However I got stuck with exercise 8.6 (2nd edition) which goes as ...
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