# Questions tagged [approximations]

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### Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
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### Is acceleration due to gravity constant?

I was taught in school that acceleration due to gravity is constant. But recently, when I checked Physics textbook, I noted that $$F = \dfrac{G m_1 m_2}{r^2}.$$ So, as the body falls down, $r$ ...
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### Can Hooke's law be derived?

Can we derive Hooke's law from the theory of elasticity? I know it is not a fundamental law and therefore can be derived from more basic considerations.
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### Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?

I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, ...
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### Why are continuum fluid mechanics accurate when constituents are discrete objects of finite size?

Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&m and gravitational forces. Presumably we model fluids as continuous objects that ...
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### Do we take gravity = 9.8 m/s² for all heights when solving problems? Why or why not?

Do we take gravity = 9.8 m/s² for all heights when solving problems?
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### What different approximations yield Gravitoelectromagnetism and Weak Field Einstein Equations?

This question is inspired by this answer, which cites Gravitoelectromagnetism (GEM) as a valid approximation to the Einstein Field Equations (EFE). The wonted presentation of gravitational waves is ...
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### Two bodies of finite size treated as two point masses in Newtonian gravity

When discussing gravitation between two bodies of finite size, for instance Earth around the Sun, we suppose the mass of Earth and the Sun to be perfectly localized at the center of each body. Is this ...
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### Near Earth vs Newtonian gravitational potential

Newton's Law of Universal Gravitation tells us that the potential energy of object in a gravitational field is $$U ~=~ -\frac{GMm}{r}.\tag{1}$$ The experimentally verified near-Earth gravitational ...
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### If the solar system is a non-inertial frame, why can Newton's Laws predict motion?

Since there is no object in the universe that doesn't move, and the solar system likely accelerates through space, how did Newton's Laws work so well? Didn't he assume that the sun is the acceleration-...
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### Eigenkets of degenerate perturbation theory

Suppose the original Hamiltonian is $H$ and we perturb it by a small potential $V$. The basis kets of the original hamiltonian $H$ contains some degeneracy. Since there's some degeneracy, we take ...
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### Is gravitational potential energy proportional or inversely proportional to distance?

We know that if an object has been lifted a distance $h$ from the ground then it has a potential energy change: $$\Delta U = mgh$$ so $h$ is proportional to $\Delta U$. However, we have also the ...
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### Is Torricelli's law “wrong” for big holes? - Tank draining problem

Consider a tank full of water with a constant cross-sectional area A1 placed vertically on the ground. Now someone drills a hole of an area A2 in the bottom of the tank, and the liquid starts escaping ...
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### Why is it OK to use electrostatics in Bohr's Model if the electron is moving?

In the Bohr's Atomic model, we have assumed the centripetal force to be provided by the electrostatic force between the proton and electron and derived the radius, energy of orbit and the velocity of ...
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### Could Navier-Stokes equation be derived directly from Boltzmann equation?

I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over ...
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### A problem of approximation [duplicate]

Possible Duplicate: Why are continuum fluid mechanics accurate when constituents are discrete objects of finite size? When we apply differentiation on charge being conducted with respect to time,...
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### Small oscillations of the double pendulum

From the Lagrangian I've got the following equations of motion for the double pendulum in 2D. (The masses are different but the lengths of the two pendula are equal.) Let $m_2$ be the lowest-hanging ...
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In deriving the quantization condition for a bound state in a potential with "no verticle walls" we start with the WKB connection formulas to find the wavefunction in the interior of the well ($x_1<... 3answers 7k views ### Why is acceleration due to gravity a constant? [duplicate] I just learned of Newton's law of gravitation and that distance between two bodies is a factor in the gravitational force. My question is if that's true why is the Earth's gravitational acceleration a ... 3answers 20k views ### How is the Saddle point approximation used in physics? I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative ... 1answer 2k views ### Is the existence of a sole particle in an hypothetical infinite empty space explicitly forbidden by QM? Suppose the universe is completely empty with one sole particle trapped in it. To simplify, I will only be looking at the one dimensional case. However, all arguments are applicable for three ... 5answers 630 views ### Mean field theory Vs Gaussian Approximation? I am getting confused about the distinction between Mean-field theory (MFT) and the Gaussian approximation (GA). I have being told on a number of occasions (in the context of the Ising model) that the ... 3answers 980 views ### Validity of mean-field approximation In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where$...
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If we introduce the notion of a massless string to denote the fact that net force on a massless string will always be $0$, since it is massless. How can these massless strings ever accelerate when ...
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### Is drag force on an oscillating sphere an effective model for a swimmer?

I saw the latest video from Sixty Symbols Little Swimmers. At the end of the videos he says that we do not know how to calculate the movement of the little swimmers. He says(6:14-6:40 in video) that ...
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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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### Relation between perturbation theory and Taylor expansion in QM

So I am looking at non-degenerate perturbation theory. The idea is that the perturbing term in the Hamiltonian is small so you somehow expand the energies and wave functions in this small term and ...
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### When to use ideal gas law in fluid mechanics?

The ideal gas law (aka the equation of state) is given by $$p/\rho_N = k_BT,$$ where $\rho_N$ is number density. When am I allowed to use this to describe a fluid?
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### Approximate cloning of a qubit, given multiple starting copies

Suppose I'm given several clones of a qubit in a pure unentangled state. That is to say, I'm given the state $(a \left|0\right\rangle + b \left|1\right\rangle)^{\otimes n}$. My goal is to make $d$ ...
330 views

### Evaluating low-temperature dependence of the BCS gap function

How does one go about evaluating the behavior of the BCS gap $\Delta = \Delta(T)$ for $T \to 0^+$ under the weak coupling approximation $\Delta/\hbar\omega_D \ll 1$? In Fetter & Walecka, ...