Derivation Definition and 1000 Threads

Hi, I'm trying to evaluate the derivates of first, second and third order of the phase change parameter in a dispersive medium. In such medium the refractive index is a function of the wavelength. In my case it depends on the wavelength in vacuum. \begin{equation*} n(\lambda_0 )\end{equation*}...

Homework Statement Hi guys, I am having a problem, knowing where to start with this question. Before I spend trying derive the partial derivative chain rule from first principles I would just like to know if this is what this questions is asking. If it is not asking that, how do I go about...

Hello all, I'm reading through Jackson's Classical Electrodynamics book and am working through the derivation of the Legendre polynomials. He uses this ##\alpha## term that seems to complicate the derivation more and is throwing me for a bit of a loop. Jackson assumes the solution is of the...

Why does it use t' in that equation and not t? Isn't the equation relative to what an observer in the external frame of reference see? So if it is why not using the time he register? (The equation is uploades in the photo)

Homework Statement 2. Homework Equations [/B] Consider a particle that is described by $$x(t)=(2.0-0.1t) \cos(0.5t)$$ and $$y(t)=(2.0-0.1t) \sin(0.5t)$$ t in seconds and x,y in meters. In previous subquestions we were asked to determine an expression for the module of the velocity vector and...

Homework Statement Using the Semi-empirical Mass Formula show that for fixed odd atomic mass number, A, the most stable isobar has a neutron to proton ratio given by N/Z = 1 + aCA2/3/(2aA) Homework Equations B(A,Z) = aV A − aS A2/3 − aCZ2A-1/3 − aA(Z − N)2/A + pairing term The Attempt at a...

Homework Statement I'm trying to understand a derivation of the Fermi-Dirac and Bose-Einstein distributions. In my textbook Thermal Physics by D. V. Schroeder it says: "The idea is to first consider a "system" consisting of one single-particle state, rather than a particle itself. Thus the...

How does the velocity at an elemental height h equates to √(2gh)? My application of Bernoulli's equation is not yielding the result. Please show the process. Thank you

Homework Statement A spherical capacitor is formed from two concentric, spherical, conducting shells separated by vacuum. The inner sphere has radius r the capacitance is C. What is the outer radius R? Already solved the problem, but I'm more wondering on how to derive the equation that I...

I have a very weak understanding of the particle modelling of electrical phenomena.1: Electric field =\frac{Force}{Magnitude of charge} 1 is The definition of electric field on a particle (?) 2: Force = \frac{Q1*Q2*K}{R^2}\\ 2 is Coulombs law, to find force between two particles. 3...

I've been reading through a derivation of the LSZ reduction formula and I'm slightly confused about the arguments made about the assumptions: $$\langle\Omega\vert\phi(x)\vert\Omega\rangle =0\\ \langle\mathbf{k}\vert\phi(x)\vert\Omega\rangle =e^{ik\cdot x}$$ For both assumptions the author first...

Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...

Homework Statement Show how one can obtain the Doppler transformation for the frequency of a receding source just using the Lorentz transformations for the energy (where E=h). Homework Equations Relativistic transformations for momentum and energy: E = γ(E' + vp'x) pc/E = v/c = β The Attempt...

Hey guys, I need your help regarding the derivation of the fourth runge kutta scheme. So, I found http://www.ss.ncu.edu.tw/~lyu/lecture_files_en/lyu_NSSP_Notes/Lyu_NSSP_AppendixC.pdf this derivation. Maybe you have a clue what tehy are doing in C.54. So before this they are calculating the...

Let's consider an isotherm isobaric adsorption of gas (A) on the adsorbent (B). There are two phases in the system: - volume phase (1) that consists of gas and adsorbent. - surface phase (2) that contains a layer of adsorbed gas on the surface of adsorbent. When deriving Gibbs adsorption...

Hi community, There is a step on the wiki page about a derivation. I don't seem to get the same thing when I try and solve for (u/c)^2 and then plug into Lorentz factor to get the new Lorentz factor so you can get the full energy momentum relation My gamma term looks more like 1/...

" We can put the Lorentz force law into this form by being clever. First, we write $$\frac{dA_j}{dt}=\frac{d}{dt}(\frac{\partial{}}{\partial{v_j}}(v.A)),$$ since the partial derivative will pick out only the jth component of the dot product. Now, since the scalar potential is independent of the...

Hey guys, I got this problem: We had the derivation of the ekman transport today in class. And what I wondered about is this: Usually the equation for the ekman transport looks similar to this (depends on the author) u = V_0 e^{az} cos(\frac{\pi}{4}+az) v = V_0 e^{az} sin(\frac{\pi}{4}+az)...

Homework Statement I'm currently working on the "cavendish" experiment and wish to use/develop a method separate from the casus we've been provided. Now I've nicely calculated and derived everything I need to know, including all the corrections that have to be made for the mass of the rod, the...

My question stems form the section "How Many Modes in a Cavity?" in the following derivation of Rayleigh-Jean Law: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html#c2" In here, they count the number of modes as represented by volume of an eighth of a sphere. What's the mathematical...

Hi. On the webpage of a lecture at the University of Virginia, I found this derivation of the magnetic force using Lorentz contraction and electrostatic force. They approximate the gamma factor to the order of ##v^2## and get the correct result. How is it possible to get to the same result...

Hi All, Mr. James Grime from Numberphile channel has said () that the Euler´s number e has basically nothing to do with geometry. I would like to know if there is any derivation of e based on geometrical arguments. Best Regards, DaTario

Homework Statement A vacuum photodiode detector utilizes the photoelectric effect to detect light. The photoelectric effect causes electrons to be ejected from a metal plate when photons of light are absorbed by the metal. The energy of a photon is given by the equation E = hf, where h = 6.6 x...

Homework Statement In Newtonian mechanics, the rocket equation is derived by solving the simple differential equation -dm U = m dV, where U is the velocity of the expelled material relative to the rocket; a matter of conservation of momentum. In order to get the correct relativistic equation...

Derive the Fokker-Planck equation by requiring conservation of probability: ∫∂VJ⋅dS=-d/dt∫Vp(r,t)dV The flux can be written as a sum of convective and diffusive terms J=p(r,t)v(r,t)-D(r,t)∇p(r,t) and substitution of this with use of the divergence theorem yields...

Homework Statement Which algebraic expressions must be solved when you use finite difference approximation to solve the following Possion equation inside of the square : $$U_{xx} + U_{yy}=F(x,y)$$[/B] $$0<x<1$$ $$0<y<1$$ Boundary condition $$U(x,y)=G(x,y)$$ Homework Equations Central...

I recently saw the derivation of length contraction in Special Relativity . At the end , it said x' = (x - vt) γ(gamma) x = (x' + vt') γ(gamma) Where γ(gamma) is Lorentz transformation . It is = 1/√(1- v²/c²) Then derivation continued , with expansion of x' = (x + vt)γ As t = 0 in this case...

Why is it needed to consider a 4D Euclidean space to introduce the FLRW metric? Is it because with a fourth parameter, we can set the radius of the 4D sphere formed with the four parametres as constant?

Homework Statement Derive E=mgh from Newton's law of Gravitation where h is very small. (Use binomial expansion) 2. The attempt at a solution E = \frac{GMm}{(r+h)^2}-\frac{GMm}{r^2} E = \frac{GMm}{r^2}(\frac{1}{(1+\frac{h}{r})^2}-1) E = \frac{GMm}{r^2}((1+\frac{h}{r})^{-2}-1) E =...

Homework Statement I am trying to derive the 2 body cross section, as given in https://web2.ph.utexas.edu/~schwitte/PHY362L/QMnote.pdf dσ/dΩ Homework Equations I am stuck on d√s/dp=v where √s=(Ea+Eb)=E The Attempt at a Solution p=Ev (relativisitic energy-momentum relationship) √s=E...

Homework Statement Show that a hollow cylinder of radius R_1, outer radius R_2, and mass M, is I=1/2M(R_1^2+R_2^2) if the rotation axis is through the center along the axis of symmetry. Homework Equations $$dm = \rho dV$$ $$dV = (2 \pi R)(dR)(h)$$ The Attempt at a Solution I was mainly...

Hoping to get an intuitive idea of the derivation behind the Rossby number that isused in fluid mechanics(atmospheric and oceanographic sciences). I know what it is and how it is used but I want to know Rossby hit upon the idea of the number that is named after him...

Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but I don't...

On page 9 of *Quantum theory of many-particle systems* by Alexander L. Fetter and John Dirk Walecka, during the derivation of the second-quantised kinetic term, there is an equality equation below: >\begin{align} \sum_{k=1}^{N} \sum_{W} & \langle E_k|T|W\rangle C(E_1, ..., E_{k-1}, W...

I am learning principle of optics written by Born&Wolf and confused with the method to derive Snell's laws and law of reflection. In the textbook,##v_1## is the speed of light in mediator 1 and ##v_2## is the one in mediator 2. ##{\vec s}## is the direction of light and ##{\vec r}## is the...

Consider the real emission correction to the tree level process ##e^+ e^- \rightarrow q \bar q## involving a final state gluon emitted from either the outgoing quark or antiquark line. The differential cross section for producing a quark with fractional energy ##x_1## in the ##q \bar q g##...

I'm an undergraduate taking a physical chemistry course, and I got to a part in my reading about the derivation of the ideal gas law. The passage is linked below...

Hi, Recently I came across this image in deriving an equation for angle of repose of an object in an inclined plane: "W" is the weight of the component which acts vertically down. "Rn" is the normal reaction by the inclined plane "W cos alpha" is the component of the weight of the object...

I've got a problem that asks us to derive the Euler-Lagrange equations by only using Hamilton's equations and the definition of the Hamiltonian in terms of the Lagrangian. Here's what I tried: The Hamiltonian is defined as \begin{align*} \mathcal{H} = \dot{q}_ip_i - \mathcal{L} \end{align*}...

The formula for the radiation pressure P in n-dimensional space for a given internal energy density u is ##\frac{u}{n}##. I would really appreciate it if someone could provide a link that gives a simple derivation of this formula for dummies like me.

Hi all - I am trying to follow a derivation of the above. At some point I need to find gαβ for gαβ = ηαβ + hαβ with |hαβ|<<1 I am stuck. The text says gαβ = ηαβ - hαβ but I cannot figure out why. Can anybody help?

I can't find a derivation of d'Alembert principle. Wikipédia says there is no general proof of it. Same with stackexchange. I find it surprising so I thought I'd come here to check with you guys. D'Alembert principle has indeed no proof ?

I was studying the derivation for taylor series in ℝ##^n## on my book and I have some trouble understanding a passage; it's the very beginning actually: ##f : A## ⊆ ℝ##^n## → ℝ ##f ## ∈ ##C^2(A)## ##x_0## ∈ ##A## "be ##g_{(t)} = f_{(x_0 + vt)}## where v is a generic versor, then we have...

Hi, I've been unsuccesfully trying to derive the Schwartzschild solution, narrowing my mistake down to a single component of the Ricci tensor. The problem is the following(taken from Weinberg's book, with grr = A , gtt = -B and the angular part being the same as in spherical coordinates): I...

Hello, I have a question about Boltzmann Distribution. I wonder why partial N of Nj is 1 and partial U of Nj=Ej. because N is constant, partial N of Nj has to be 0 and Partial Nj of U has to be 0 as well. They are constants so, to make sense of the equation, alpha and beta have to be 0 but...

Homework Statement When an applied force elevated at angle θ is used to drag mass m along a surface with μ as the coefficient of friction, the mass accelerates horizontally with some value, a. Derive the cleanest and most simplified formula for the applied force, Fapplied, that will give the...

Hi guys, I was hoping that someone might be able to help me out with a formal derivation of this common thermodynamic equation regarding the change in entropy during an isothermal change of state. The first equation is what I would like to derive, and the second is where the book tells me to...

Homework Statement How to derive eq.3.34 in Lancaster's book QFT for the gifted amateur Homework Equations ##\hat H= \int d^3 p E_p\hat a\dagger_p\hat a_p## The Attempt at a Solution Comparing

Homework Statement Where U is potential energy, show that F = -du/dx Homework Equations ΔU = U(x) - U(x_0) $$ΔU = U(x) - U(x_0) = \int_{x_0}^{x}Fdx \qquad (1)$$ The Attempt at a Solution [/B] I am confused why $$\frac{d}{dx}ΔU = \frac{du}{dx} \qquad (2)$$...

Hi, Could someone please tell me how to derive this formula by using Wave Phenomenon d = t sin θ [ 1 - (n cosθ / n' cosθ)] I think some of it is derived using Brewster's Principle and the Refractive Index but I cannot tell how? Thanks.