# Questions tagged [approximations]

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### Small Angle Approximation for Simple Pendulum

I am working on a simple pendulum problem. The $y$ direction is vertical and the $x$ direction is horizontal. Displacement in the $x$ direction is taken to be much less than the length of the string, ...
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### What is a quasistationary approximation

I was reading an article which states : The linear-stability analysis for this system can be performed in complete generality; but it will be best for purposes of this review to go directly to ...
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### Why should the spherically asymmetric part of the effective potential be small in the central field approximation?

In the central field approximation, each electron is supposed to move in an effective or average potential contributed by its attractive interaction with the nucleus and repulsive interaction with the ...
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### What do the small terms in the series expansion of relativistic energy mean?

Through the fabulous Feynman Lectures of Physics and the introduction of relativistic mass, Richard Feynman made a link between the increase in kinetic energy of a heated molecule of gas, and its ...
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### Composite particles Dirac spinor approximation

In many scattering process evolving composite particles such as proton, the composite particles are treated as an elementary particles. For example in electron proton scattering to the proton is ...
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### Taylor expansion of scalar fields [closed]

Starting of with electrodynamics I have to compute the taylor expansion around $\vec{r} = 0$ of $\psi (\vec{r}) = |\vec{r} - \vec{r_0}|^{\frac{3}{2}}$ where $\vec{r_0}$ is a constant vector up to ...
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### Kepler's Second Law: Why do we calculate the area of a triangle rather than the area of a sector?

Kepler's Second Law states that equal areas are swept in equal times. When calculating this area, why do we use the formula for the area of a triangle rather than the area of a sector?
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Generally the path difference between two rays is considered as dsin$\theta and for this generally the two rays are considered parallel. That is shown in diagram 'c'. My questions - 1. is even ... 1answer 106 views ### Can anyone explain the harmonic oscillator (in context to quantum mechanics) 2.3 (Griffiths) using Taylor series? At the end he concludes$V(x) = V''(x_0)(x-x_0)^2$. How does he get to know that the rest are$0$? How does he conclude$V''(x_0) = k$. Please try to explain in easy ways and tough vocabulary. I don't ... 3answers 64 views ### Regarding assumptions In most of the theories or derivations we take some assumptions like has is ideal, frictionless piston and many more but these are not applicable in real world. But in our real life situations we ... 0answers 40 views ### Anomalous curvature coupling corrections for$Dp$-branes worldvolume actions The Chern-Simons term of an (abelian brane) is commonly written as $$\sim\int_{\mathcal M_{p+1}}\sum_iC_{i}[e^{2\pi\alpha'F+B}],$$ where$C_i$is the background Ramond-Ramond$i$-form,$F$is the ... 1answer 83 views ### When and why are we allowed to treat a rigid body as a point mass? When the subject Mechanics first taught, it is common that we explicitly state that the Newton's laws are valid only for point masses, and then we give examples of rigid bodies colliding with each ... 0answers 65 views ### Has anyone ever actually considered a spherical cow? [closed] Yes, I'm aware this question is somewhat whimsical. I'm sure every physicist is familiar with "Consider a Spherical cow". Has a cow (or any animal for that matter) ever been assumed spherical for ... 1answer 66 views ### Vacuum Conditions in teaching high school physics I'd like to know why in high school physics is taught mostly in vacuum conditions instead of terrestrial ones. I don't mean one is more important than the other, but it's just a curiosity about that. 2answers 74 views ### Conservative$E$-field and Kirchoff rule in practice In undergrad physics, when analyzing an LR circuit, it is often considered that Kirchoff rule holds. However, as far as I understand, Kirchoff rule only holds when E field is conservative (curl of E ... 2answers 384 views ### How can we justify, in deriving quantum statistics, the use of Stirling approximation in the form$\ln(x!)\approx x \ln x - x\$?

At first sight one can say "why not to use only one term, or maybe three or more terms"? Why use two terms? I see that books (see for example good books like Griffiths quantum mechanics or Atkins ...