# Questions tagged [approximations]

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### How to approximate friction coefficients between different materials?

I want to add friction forces to my computer game. I know there are tables for friction, however I don't think that encoding big table of coefficients (of size $n^2$) is a good idea. I thought, that ...
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### How to justify RPA (random phase approximation)?

The Random Phase Approximation (RPA) is a technical method used in field theory to account for interactions when calculating correlation functions. It consists of only keeping a certain class of ...
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### Validity of the sudden/diabatic approximation

The Schrodinger equation is given by $$i\hbar\ \frac{\partial}{\partial t}\ \mathcal{U}(t,t_{0})=H\ \mathcal{U}(t,t_{0}),$$ where $\mathcal{U}(t,t_{0})$ is the time evolution operator for evolution ...
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### Quantum Gravity In Particle Accelerators

It is my understanding that we have no fully working model for Quantum Gravity. However, I imagine one would need to take quantum gravity into account when making discoveries in, say, particle ...
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### Obtaining Transmission Coefficient of Beam Upon a Linear Potential

I would like to determine the transmission coefficient $\mathcal{T}$ for a particle beam $$\Psi(x,t) = A_o e^{ikx}e^\frac{-iE_ot}{\hbar}$$ with energy $$E = \frac{\hbar^2k^2}{2m}$$ incident upon a ...
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### Is the adiabatic theorem in Quantum mechanics valid in general for Non-Hermitian Hamiltonians?

Is the adiabatic theorem in Quantum mechanics valid in general for Non-Hermitian Hamiltonians? The proofs I have come across for adiabatic theorem all assume at some point in the proof that the ...
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### Time averaging a Hamiltonian

There are a number of problems in quantum mechanics whose solution relies on time-averaging away parts of the Hamiltonian. In particular, two examples that come to mind: The rotating wave ...
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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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### Planck's theory question

Could you please tell me why Planck's theory ceases to be valid when the sizes of the bodies and/or their separation distances are comparable to, or smaller than, the wavelength. My professor told me ...
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### Idealizations of an object as a point particle

Why is it that an object can be idealized as a point particle or 'particle like' to solve problems? What are the limits of such a tool?
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### Velocity between two running animals

One animal $A$ can run $100$ km/h and another animal $B$ can run $85$ km/h. Suppose the slower animal $B$ starts running $25$ meters ahead of the faster animal $A$ in a direction. How can I ...
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### Can there be tension in an inextensible string?

In physics, tension describes the pulling force exerted by each end of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-...
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### Velocity of small oscillations

We consider that the displacements about equilibrium are small, in small oscillation. Do we also tacitly assume that the velocity (rather, its magnitude) remains small as well? In Goldstein, it's ...
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### Is $\pi^2 \approx g$ a coincidence?

In spite of their different dimensions, the numerical values of $\pi^2$ and $g$ in SI units are surprisingly similar, $$\frac{\pi^2}{g}\approx 1.00642$$ After some searching, I thought that this ...
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### Point object, Kinematics

I am very new to physics. This evening, I was reading about the concept of objects to be considered as point objects under some circumstances. And I was trying to think of circumstances under which ...
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### WKB approximation to find energy levels of a step potential

Suppose the following potential: $$V(x) = \begin{cases}V_0 & 0<x<\frac{a}{2} \\ 0 & \frac{a}{2}<x<a \\ \infty & \text{otherwise} \end{cases}$$ Also, assume that for every ...
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### Difference between naive and Coriolis-force calculation

Consider the classical problem of dropping a coin from a tower at the equator of a planet without atmosphere and with spin $\Omega$: where in relation to a plumb-line will the coin land? When doing ...
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### Adiabatic approximation with scaled time?

In this article (page 3) they have following expression for the coefficients in the adiabatic approximation: \dot a_k(t)=-a_k(t) \langle k| \dot k \rangle -\sum_{n\ne k} a_n(t) \frac{\langle k(t)|\...