# Questions tagged [approximations]

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2answers
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### Is the harmonic oscillator approximation valid in occasion of very powerful fields?

I noted that in physics, to study electromagnetic wave phenomena when there is a sinusoidal behaviour, often is used the approximation of harmonic oscillation. I tried to understand the basics of why ...
1answer
191 views

### How can I find the metric in weak field limit for specific theory?

What is the general approach to finding a modified version of Poisson equation by means of the weak field limit of a specific gravitational theory? What is the first step? Can you introduce the main ...
2answers
117 views

### Violating Quantization of Charge?

Isn't it the violation of "the quantization of charge" when we use $dQ$ for calculation like integration or derivation?
2answers
428 views

### Why are angular velocities of double pendulum small in small angle approximation? [duplicate]

In the lagrangian for double pendulum for small angles, the term $\dot{\theta}_1\dot{\theta}_2 \left [ 1-\frac{(\theta_1-\theta_2)^2}{2} \right ]$ is replaced with $\dot{\theta}_1\dot{\theta}_2$, ...
2answers
124 views

### Are some laws in physics really as simple as they seem?

For example, is $F = ma$ really an exact formula, or is it an approximation? I know a lot of formula's come from taking the first few terms of a Taylor expansion, so I was wondering if the simple ...
1answer
47 views

### Neglecting some wave functions by assuming that the angle between tension force and horizontal is small in the derivation of wave equation in $1D$

In the derivation of the wave equation in classical mechanics in one dimension in a string. It's assumed that the angle between the tension and the horizontal line is small. This is assumed to allow ...
2answers
911 views

### Why does GW-DFT give higher bandgaps in semiconductors

Usually the GW Density Functional Theory (DFT) gives larger band gaps in semiconductors compared to the LDA and GGA methods. This seems to be related to the screened potential in GW, but it is not ...
1answer
70 views

0answers
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### How does approximations to assumptions lead to approximations to solutions?

I was reading Physics SE 228313. It talks about using Born-von Karman condition to model metal lattices. Is there any mathematical justification that approximations to physical condition would give ...
3answers
79 views

### Oscillator with decaying restoring force

Suppose a system that is described by the equation of motion: $$\ddot{x} = -k\cdot x\cdot \exp\left(-\frac{t^2}{2\sigma^2}\right).$$ (For example a spring with decaying stiffness.) I'd like to ...
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
81 views

### Why does mass increase when gravitational potential energy increases?

I saw a solved example in a book (Concepts of Physics by H.C. Verma, volume 2), where there is a body near surface of the earth, the problem is to calculate the increase in mass of the body when it is ...
0answers
106 views

### Validity of the thin wall approximation

Inspired by the question How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?, I decided to come back to the first paper by ...
0answers
27 views

### Maximum intensification by refraction

Suppose that a beam of light in a medium with index of refraction $n$ reaches the surface of the medium, with vacuum on the outside. Its incident angle with respect to the normal is $\theta$. Only a ...
0answers
298 views

1answer
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### Approximate formula for the volume of water at a given temperature

Sorry for asking this kind of question. Do you recongnize this formula? $$V(T) = 0.0000679T^3+0.0085043T^2- 0.0624T+999.87$$ when $V$ is volume of water in $\mathrm{ml}$, $T$ is temperature in ...
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### Hyperfine structure in hydrogen

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. ...
0answers
129 views

5answers
575 views

### Why does a massless, frictionless piston move from high pressure to low pressure?

Consider an ideal gas kept in a rigid cylinder with a movable massless, frictionless piston at the top. Let the pressure inside the cylinder be $P$ at pressure exerted by the surrounding on the ...