# Questions tagged [approximations]

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### Is Stokes equation a reduction of Navier-Stokes equations?

The following Stokes problem: $$\begin{cases}-\nu\Delta u+\nabla p=f&,\textrm{in }\Omega\\ \nabla\cdot u=0&, \textrm{in } \Omega\end{cases}$$ is a reduction of the Navier--Stokes equations? ...
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### 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 ...
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### Theoretical justification for the range of validity of the approximation $R(T)\approx R(T_0)[1+\alpha (T-T_0)]$

In the experiment for calibrating a platinum resistance thermometer, we are always approximating the resistance of the platinum thermometer by $$R(T) \approx R_0 (1+\alpha T),$$ taking the reference ...
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### “Newtonian limit” property of special relativity

Books say that special relativity is indistinguishable from Newtonian mechanics when the speed of the primed frame ($v$) is small compared to the speed of light ($c$). This is what I mean by the "...
197 views

### First-Order Perturbation of Energy Eigenfunction

I have a homework questions where I'm struggling to understand the methodology to use. We derive first the energy functional for the energy eigenfunction equation (this is fine, I used some vector ...
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### What is the mathematical approximation for uniform gravitational field in Newtonian Mechanics? [duplicate]

When measuring the local gravitational field using a simple pendulum, one of the core assumptions is that the gravitational field is homogeneous. But the theory itself (Classical/Newtonian Mechanics) ...
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### What is the static exchange approximation?

In this paper, on the 4th page (and throughout), they talk about studying electron-helium scattering in the "static-exchange approximation". I have scoured the literature and have not been able to ...
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### problem with Sudden Approximation in quantum mechanics

If the Hamiltonian of a system changes abruptly (over a very short time interval) from one form to another, we would expect the wave function not to change much, yet its expansion in terms of the ...
132 views

### Series expansion of $N$-particle potential energy

I am trying to understand the so-called Taylor expansion (or series expansion) of potential energy of a system of $N$-particles. This expanded form is stated without derivation in some molecular ...
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### Calculating Total energy of 2D Debye monoatomic solid

I am trying to find the total energy of a mono-atomic 2D Debye solid. I started with the density of states: $$D(\omega)=\frac{A\omega}{\pi c^2}$$ where A is the area, $\omega$ the frequency and c ...
197 views

### Second order relativistic corrections to Pauli equation from Dirac equation

I'm trying to derive the full and correct Hamiltonian for spin$\frac{1}{2}$ particles from Dirac equation up to second order in $v/c$. For a potential and magnetic field constant in time. In ...