# Tagged Questions

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### Why Earth is considered to be an inertial frame? [duplicate]

Earth rotates about its axis and also revolves around the Sun at the same time. So why Earth is considered as an inertial frame in Newtonian Physics. So technically, I'm effectively asking why the ...
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### Why is the elemental volume of a sphere equal to $4 \pi r^2dr$?

I was doing this question on calculating the electric field at a certain point in a sphere (length $r$ away from the centre), where the charge density is given by an equation. When I checked the ...
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### What is the typical strength of the electric field in a particle accelerator?

I am working on a research project involving the closed orbits of hydrogen in the presence of an external electric field and I am curious what a reasonable approximation for the electric field ...
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### WKB boundary conditions [duplicate]

Technically, this is a math problem but I think it is better here than in the math stacks. Consider the differential equation $$y'' = (x^4 - E)y$$ The boundary ...
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### Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation $$i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi$$ using the variational relation \begin{...
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### Lagrangian for small oscillations

For a double pendulum we can consider 2 generalised coordinates $\theta_1$ (angle between first mass and vertical axis) and $\theta_2$ (angle between second mass and vertical axis). The Lagrangian to ...
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### Hartree-Fock: Coulomb integral [closed]

Today I was wondering how to better understand the Coulomb integral in the Hartree-Fock approximation. Extracted from: Szabo & Ostlund, Modern Quantum Chemistry, p. 112 The Coulomb term has ...
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### 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 ...
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### Weizsäckerâ€“Williams approximation

I'm having some trouble understanding the WeizsĂ¤cker-Williams approximation What I think it is is the following: I have a charged particle at high speed, close to the speed of light, at this speed ...
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### Born approximation and dipole approximation

I'm having some trouble really understanding when it's okay to use these approximations and why. I've been looking myself blind on equations, but I'm not even sure I understand it qualitatively. So I ...
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### Energy levels in close-proximity of each other in time-independent degenerate perturbation theory

I've applied second order time-independent degenerate perturbation theory corrections to the energy with the method presented in Modern Quantum Mechanics by J.J. Sakurai. I shortly summaries this ...
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### Where do we get the terms involving $\Phi$ in parentheses come from in the static weak field metric?

I am confused about the static weak field metric. As written in Hartle, it reads ds^2 =-\left(1+\frac{2\Phi(x^i)}{c^2}\right)(cdt)^2 +\left(1-\frac{2\Phi(x^i)}{c^2}\right)(dx^2+dy^2 ...
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### 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 ...
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### 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 SchrĂ¶dinger equation (without the $\hbar$ and such). However, in the ...
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### What is the range of validity of Fermi's Golden Rule?

It is well known that to calculate the probability of transition in the scattering processes, as a first approximation, we use the Fermi golden rule. This rule is obtained considering the initial ...
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### Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
Using mean-field theory, the magnetization per spin, $M$, for a ferromagnet always obeys the equation: $M=\frac{g \mu_{\mathrm{B}}}{2}\mathrm{tanh} \left( \frac{2}{g \mu_{\mathrm{B}}} \frac{T_{\... 1answer 53 views ### What do we get from the diagonalization of the$k\cdot p$matrix? In k.p theory, we expand the wave function around a known point${\bf k}_0$$$u_{\lambda}({\bf k})=\sum_{\nu} c_{\lambda,\nu}({\bf k})u_{\nu}({\bf k}_0).$$ If we now consider 8 bands (conduction, ... 1answer 89 views ### Post-Newtonian approximation for binary gravitating system I have been studying gravitation waves radiated by a binary source. I have linearised Einstein's field equation and approximated the source to a Quadrupole moment to get the power radiated by the ... 0answers 68 views ### How can the fictitious mass in the Car-Parrinello method reproduce the “real” dynamics? In the Car-Parrinello method, to solve simultaneously the classical equations of motion for the atoms and the Kohn-Sham equations for the electrons, the following effective Lagrangian is used:$$\tag{... 1answer 209 views ### Why can we not apply perturbation theory in Born-Oppenheimer approximation In Weinberg's Lectures on Quantum Mechanics, he mentions Unfortunately, we cannot simply use first-order perturbation theory, with$T_{nuc}$taken as the perturbation and the state vectors$\Phi_{...
When does the macroscopic continuum description of a medium like a fluid break down? Say I'm interested in a scattering process of some particles with momentum $p$ and energy $E$ off a fluid of ...