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Results tagged with perturbation-theory
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user 1325
Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.
3
votes
Accepted
Fine Structure Degenerate Perturbation Theory Hydrogen
In my 1995 edition the text (on page 242) reads:
So presumably this is an error in whatever edition you have.
- 363k
5
votes
Accepted
What can be the smallest chaotic system?
A hydrogen atom can be made to show chaotic behaviour if it is excited to very near it's ionisation energy. The maths is somewhat beyond me, but this paper discusses calculations of the hydrogen atom …
- 363k
3
votes
Accepted
Most suitable metric for the Solar system?
Solving the Einstein equation for a system as complex as the Solar System could only be done numerically, and in any case it's not terribly useful. Nothing in the Solar System, is relativistic enough …
- 363k
3
votes
What does the term $\mathcal O(\epsilon^2)$ mean?
$\mathcal O(\epsilon^2)$ just means of order $\epsilon^2$ i.e. terms that are proportional to $\epsilon^2$.
The point is that is $\epsilon$ is much less than unity then $\epsilon^2 \ll \epsilon$, so …
- 363k
22
votes
Accepted
Staying in orbit - but doesn't any perturbation start a positive feedback?
An orbit is stable because of conservation of angular momentum.
Suppose we start with an object in an exactly circular orbit and slow it down slightly. That means it is moving at less than orbital ve …
- 363k