# Questions tagged [approximations]

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### How is the gravitoelectromagnetism approximation of GR valid if it seems to yield unstable solutions?

In the gravitoelectromagnetism approximation of GR, we have equations analogous to Maxwell's equations with some sign changes. As pointed out in another post of mine, this leads to unstable run-away ...
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### The multipole expansion of electrostatic potential and large distances

I'm reading Griffiths electrodynamics book and I'm currently studying the multipole expansion of electrostatic potential, and I have two questions if you don't mind: Can I use the multipole expansion ...
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### Kinetic friction and damped harmonic oscillators

I was taught in school that the magnitude of the kinetic frictional force does not depend on the speed. Hence, the equation of motion of the harmonic oscillator in the presence of friction with the ...
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### How small is $dt$ in this derivation of the kinetic energy of ideal gasses?

I was reading the derivation of the average translational kinetic energy of an ideal gas in Sears and Zemansky's University Physics. This derivation uses a cylinder with height $|v_{x}|dt$ and base ...
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### Is the drag force to raindrops at the terminal velocity quadratic or linear?

Air drag is approximated by the following equation $$F=\frac12 \rho A v^2 C_D$$ Depending on the drag coefficient $C_D$, this force may be linear or quadratic with respect to velocity $v$. If $v$ is ...
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### Equation of motion with air resistance

If I search for air resistance on a falling object, I find texts stating that it is proportional to the velocity. $$F=mg-kv$$ Is this accurate or approximate? Some texts say that when the speed is ...
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### Can the cases of multiple fermions in any spherically potential be approximated by the Schrodinger Equation for a single fermion?

In this video https://www.youtube.com/watch?v=tq_y1qOmUBE&t=783s it's mentioned that the structor of atoms of multiple particles can be approximated using the Schrodinger Equation of the Hydrogen ...
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### Expansion of $\phi (x)$ in the derivation of WKB approximation

In the derivation, we assume the eigenfunctions of $H$ to have the form $$\psi (x)=e^{i \phi(x)/\hbar}$$ where $\phi (x)$ is allowed to take any complex value. But then suddenly we assume this ...
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### When can you trust first-order QED?

In QED, we use the perturbation expansion. Usually, we use the first-order perturbation expansion, and sometimes the second. I want to know, physically, what conditions need to be satisfied for us to ...
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### Is the continuum limit equivalent to the low-energy limit?

It is frequently stated that the continuum limit of a lattice model is equivalent to the low-energy limit, e.g. here, here and section IIB of this. I do not know how to show this for myself. Take for ...
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### Function Values Surrounding Stationary Points

Taylor, in his widely read book "Classical Mechanics," writes on page 218 that When $df/dx = 0$ at a point $x_0$, but we don't know which of the 3 possibilities obtains, we say that $x_0$ ...
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### Does the stationary phase approximation equal the tree-level term?

Consider the scalar field transition amplitude $$\tag{1} \mathcal{A} = \int_{\phi_i}^{\phi_f} D\phi e^{iS[\phi]/\hbar}.$$ Let $\phi_{cl}$ solve the classical equation $\frac{\delta S}{\delta\phi}=0$. ...
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### How large does $N$ need to be for statistical mechanics to be a good approximation?

About how many components ($N$) does a system need for statistical mechanics to apply to that system? I took stat mech and biophysics from the same professor in undergrad and I distinctly remember him ...
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In this1 paper they use an adiabatic approximation to reduce two differential equations to one. Could you please recommend some alternative reading for this (semi) classical adiabatic approximation, ...
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### Wood-Saxon Potential approximated to Harmonic-Oscillator Potential

Under what assumptions does a Wood-Saxon Potential for a nuclear bound state be approximated as a Harmonic Oscillator Potential?
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### If there is no perfect black body then what's the point of learning about it? [closed]

My question is simple if there is no perfect black body then what's the point of learning about it? Because definition of balck body goes like this A body which can absorb and re emit all kinds of ...
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### Converting between mass and binding energy in semi-empirical mass formula

The semi-empirical mass formula is given in terms of the binding energy as: $$B(Z,N) = aA - bA^{\frac{2}{3}} - s \frac{(N-Z)^{2}}{A} - d \frac{Z^2}{A^{\frac{1}{3}}} - \frac{\delta}{A^{\frac{1}{2}}}$$ ...
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### Perturbation theory and size of the perturbation

In quantum field theory, we usually perturb the free field by a little bit. What would be so bad about using a large perturbation to the free field?
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### Justification for constant tension in transverse wave on a string

It is common in the derivation of the transverse wave equation on an ideal string to assume the tension along the rope is uniform in the limit that $$|\partial \psi / \partial x|\ll 1.$$ However, what ...
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### Is the Newtonian gravitational potential $-\frac{GMm}{R}$ just an approximation?

Is $-\frac{GMm}{R}$ just an approximation? I believe that it is since we assume that one of the mass is at rest when deriving it.
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It is often said that the Dynamical Mean Field Theory (DMFT) does not take into account spacial correlations. What does this mean in layman terms? Does that mean that we assume:  \langle n_i n_j \...