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2answers
42 views

Wave speed derivation

The wave speed derivation approximates the wave as a circle. It uses that to know that a=v^2/R. However, numerous functions can approximate the wave. A straight line, x^2, x^3, etc. If I used those I ...
7
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1answer
408 views

Adiabatic approximation

The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down. As it is based on the idea of the nuclii being much heavier than the electrons I ...
3
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1answer
288 views

'Validity' of QED/QCD/Electroweak interaction

I am currently attending a course on Quantum Field Theory and I got into thinking how valid these theories are. As the theory attempts to describe reality only far above the Planck (length) scale, ...
1
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1answer
27 views

About field lines and continuity of magnetic and electric fields

In my laboratory class we were doing an experiment with grass seeds and iron filings to visualize the electric and magnetic field lines. So, we were discussing why they appear, because we know that ...
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1answer
81 views

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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1answer
54 views

Am I using the variatonal method correctly conceptually?

Given A particle in a potential well: $V=-V_0 \exp(-x^2 / L^2)$ Goal Use the variational method to approximate the ground state energy My proposal The well (For $L=1$ and $V_0=10$) has the following ...
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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, ...
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0answers
128 views

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 ...
3
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0answers
36 views

Why is stat mech involved in mean field theory?

Mean field theory involves approximating an interacting system by a non-interacting one, by replacing some operators with their expectation value. However, to my surprise, free energy is involved in ...
3
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0answers
314 views

What does it mean to expand a Hamiltonian using perturbation theory?

On UC Davis chemwiki website, the Hamiltonian for quadrupolar coupling in NMR is analyzed. (The details of this aren't important.) It is said in the analysis that: The expansion of the ...
3
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0answers
333 views

Born approximation to Lippmann-Schwinger integral equation

I am having the following problem understanding the Born approximation in the case of the Lippmann-Schwinger equation. This exercise is for something which is entitled "computational physics lab ...
2
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0answers
63 views

Numerical problem with Hartree-Fock equations for dilute Bose gas

I have to solve the following set of equations self-consistently: $$\begin{align} n_c(\mathbf{r}) & = \frac{1}{g}\left[\mu - V_{\rm ext}(\mathbf{r}) - 2 g n_{T}(\mathbf{r}) \right] \\[3mm] n_{T}(\...
2
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0answers
61 views

Hyperfine structure in hydrogen

Consider the Dirac equation for bounded electron in hydrogen atom. I am trying to get a clear physical explanation for all mathematical terms that appear in the Hamiltonian and energy spectrum. ...
2
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0answers
66 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{...
2
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0answers
80 views

Why does the time-independent perturbation theory become no longer useful when its order gets larger?

In Griffith's Introduction to Quantum Mechanics p. 256, after figuring out $$E_n^2=\sum_{m\neq n} \frac{|\langle\psi_m^0|H'|\psi_n^0\rangle|^2}{E_n^0-E_m^0}$$ he says We could go on to calculate ...
2
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0answers
183 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
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0answers
21 views

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)|\...
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0answers
57 views

Approximate cloning of a quantum state, informed by past measurements

Suppose I give you a state $|\psi\rangle$, and tell you a sequence of measurements that have been performed on it. The measurements are not guaranteed to be orthogonal to each other, or to cover the ...
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0answers
33 views

Taylor expansion with fractional powers

A while ago, I was doing a physics problem, expanding to first order in a small parameter $x$, when I got an answer of $\cos^{-1}(1-x)$. This function blows up if you take a Taylor expansion, because ...
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0answers
30 views

Approximating Gallons of Gas Needed for Trip (read: physics grad. with too much free time)

My departure from college has left me with an itch for physics-y problems to solve, and my boredom and free time gave way to this approximation of the gallons of gas I use for the trip to my ...
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0answers
101 views

Fresnel diffraction approximation (parabolic waves)

The Huygens-Fresnel principle (Introduction to Fourier Optics, Goodman), $$ U(x,y)=\frac{z}{i\lambda}\int_\Sigma U(\xi,\eta)\frac{e^{ikr}}{r}d\xi d\eta\,, $$ where $\cos \theta=\frac{z}{r}$, shows ...
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0answers
40 views

Approximate Electric Potential $V$ so that it is of the form $V(r) + V(\phi) + V(z)$

I'm trying to simulate the conductivity of a nanowire that is modeled by a cylindrical shell of infinite potential with benzene rings in the core of the wire. (This is based on a coiled-coil protein ...
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0answers
66 views

I have a problem with the variational method approximation in quantum mechanics. Is my issue valid, or am I misunderstanding something?

The variational method for approximating the ground state of a Hamiltonian $H$ by providing a lower bound is simple enough. If we construct any test wave function $|\bar{0}\rangle$ then the claim is $$...
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0answers
56 views

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 ...
1
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0answers
84 views

Weizsäcker–Williams approximation

I'm having some trouble understanding the Weizsäcker-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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0answers
66 views

Applying Statistical Mechanics to Formulate Corrosion (Rusting)

I wanted to try and take my current knowledge of statistical mechanics (first quarter undergraduate course completed, beginning researcher in far from equilibrium statistical mechanics, basic ...
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0answers
61 views

Does Planck's constant imply limits to computing *results*

... I don't mean quantum effects limiting hardware fabrication sizing. Such small scales have for some time exhibited issues. Rather, along the lines of imagining the smallest possible divisions of ...
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0answers
458 views

Adiabatic approximation and time-dependent problems

I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand it....
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0answers
142 views

Can anyone outline the theory of plane wave Born approximation for direct nuclear reactions in detail?

Can anyone outline the theory of plane wave Born approximation for direct nuclear reactions in detail? Also What are the modification introduced in the distorted wave Born approximation? I was ...
1
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0answers
310 views

2D quantum well energy spectrum (analytical vs numerical)

I am trying to understand the energy spectrum difference between the analytical and the approximated solution for a quantum well. The particle is inside a box with domain $\Omega=(0,0)$X$(1,1)$. For ...
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0answers
128 views

Measurement in Quantum mechanics

I have got a quantum conservative system whose Hamiltonian is $H$. I consider an selfandjoint operator $O$ whose eigenvalues and eigenvectors are: $$O|\psi _{n}\rangle = \lambda _{n}|\psi _{n}\rangle$$...
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0answers
175 views

Hooke's Law and the shape of coils

I've learned in school that the force in a coil is $F=kx$, linear on how much the coil is stretched. Two questions: Is it always linear for every shape of a coil? Does it remain linear if we ...
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0answers
152 views

Question on energies obtained via WKB approximation

Suppose we are given an ODE problem $$ y''(x)+V(x)f(x)=E_{n} y(x) $$ with boundary conditions $ y(0)=y(\infty)=0$. Here $V(x)$ is a potential function. Then is it always true that (for $n \...
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0answers
24 views

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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0answers
30 views

Fermi's golden rule and the DoS of scattering states

Can the Fermi's golden rule $$\Gamma_{fi} ~=~ \rho(E_f) \frac{2\pi}{\hbar} |M_{fi}|^2$$ be applied for transitions of discrete states to scattering states? If yes, then what should the density of ...
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0answers
22 views

Multipole expansion of the electric field generated by an infinite charged plane

Take an infinite plate with uniform charge density, the classical problem that is usually solved with Gauss' theorem, to get that the electric field outside the plane, at a point $\boldsymbol r$ is: $$...
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0answers
52 views

Is the Fermi golden rule really accurate for calculating the life time of an atomic level?

In my impression, Fermi golden rule is routinely used in calculating the life time of an excited atomic level. But it is based on the first order perturbation theory, so it is not expected to be ...
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0answers
27 views

Systems with elements having size which tends to zero

[Question] If I have an element whose size(as in physical dimensions) tend to 0 but is NOT 0 (very very very small). If I create a system from these elements based on (say) the fractal concept (...
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0answers
135 views

How does a ball cause a splash? (With the relevant math)

Problem Statement: Imagine a spherical ball is dropped from a height $h$, into a liquid. What is the maximum average height of the displaced water? For instance, although one particular drop of water ...
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0answers
39 views

Off-axial Field of Finite Solenoid

Regarding the computation of the off-axial field of a finite solenoid: The Radial and Z components of the off-axial magnetic field of a solenoid are given as: \begin{align} B_r &= \frac{\mu ni}{\...
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0answers
34 views

Atmospheric refraction approximation

I am studying atmospheric refraction, reading ITU P.834 Effects of tropospheric refraction on radiowave propagation, and I have a question about an approximation. They say that refraction correction, $...
0
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0answers
120 views

Point source approximation

I have a 0.05 mm radius sperical source of Photons, and a 10 mm X 10 mm detector aligned to be orthogonal to their distance vector. Distance is D $\approx$ mm. I want to know how good the point ...
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0answers
103 views

How to get general relativity from linear gravity theory?

I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the self-interaction(...