# Questions tagged [approximations]

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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 ...
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### 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 ...
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### Violating Quantization of Charge?

Isn't it the violation of "the quantization of charge" when we use $dQ$ for calculation like integration or derivation?
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### 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 $\dot{\theta}_1\dot{\theta}_2$, ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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. ...
The variational method for approximating the ground state of a Hamiltonian $H$ by providing a lower bound is simple enough. If we construct any test wave function $|\bar{0}\rangle$ then the claim is $$... 0answers 87 views ### How fast do I have to dry myself for a hot shower to heat my body? I am not a physicist. I would like to know how fast do I have to dry myself after taking a hot shower to get more heat from the shower, than lost because the water on my skin increasing heat exchange ... 0answers 84 views ### WKB formula and Langer correction [duplicate] The general WKB approximation formula states that$$ \int_a^b\sqrt{E_k-V(x)} = (k+1)\pi \text{ with } x \in [a,b] $$for a regular Schrödinger equation (without the \hbar and such). However, in the ... 1answer 572 views ### Proof of the conservation of the energy functional for the Gross-Pitaevskii equation? From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation \begin{... 0answers 769 views ### Adiabatic approximation and time-dependent problems I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand it.... 0answers 408 views ### Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for \ell=0 using the WKB approximation. I am sure that I set up the integral ... 3answers 619 views ### Index of Refraction in Metal: Approximating Complex Perturbation If you consider waves in a metal, you can write the index of refraction for the metal as,$$ n^2 = 1 - \frac{\omega_p^2}{\omega^2} $$I am interested in what will happen if the index is perturbed by ... 3answers 186 views ### Why do we invent non-physical concepts (like e.g. point particles) to study physical phenomenons? There is nothing exist like point particles in reality then why did we invented the notion of point particles and how does it relate to real world? 4answers 125 views ### Approximations of the kind x \ll y [closed] I have an expression for a force due to charged particle given as$$F=\frac{kQq}{2L}\left(\frac{1}{\sqrt{R^2+(H+L)^2}}-\frac{1}{\sqrt{R^2+(H-L)^2}}\right) \tag{1} where $R$, $L$ and $H$ are distance ...
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 ...