Derivation Definition and 1000 Threads

I understand Runga Kutta 4th order for use with a single ODE, but am not confident I have correctly derived how to apply RK4th to a coupled or 2nd order system. As example I have dy/dt=p; dp/dt=-4pi2y I recognize this as SHM with w=2pi so yes, I don't need RK to solve it, but I want to use...

Hi, I am struggling with a particular point on the derivation of the kinetic theory of gases. Between 5mins and 6mins 30seconds of the video below they discuss how to get a value for the average of the squared velocities of the molecules in the gas. The bit I don't get is why they divide by 'N'...

My quantum course starts with the Rayleigh-Jeans law derivation. Whilst I understand most of this, I'm not sure why the average energy of each mode is equal to what they say it is. For instance here is one explanation from hyperphysics: Assigning energy to the electromagnetic standing waves in a...

Homework Statement In the inverse compton scattering, find the formula of the recoiled electron as a function of the incoming electron Homework Equations The energy of the incoming photon and electron are known. The Attempt at a Solution Starting from this...

I was reading "The foundation of the general theory of relativity" by Albert Einstein. I faced some difficulty to understand his derivation of "geodetic line", stated in "The equation of the geodetic line. The motion of particle" headed section. I will try to describe my problem clearly and in...

When the ideal gas entropy is derived, we consider N atoms in a box of volume=Lx*Ly*Lz. Then, we make the assumption that Lx,Ly,Lz >>de Broglie wavelength of atoms. I am not sure why we need to make this assumption? Thanks!

I'm looking at: http://arxiv.org/pdf/gr-qc/9712019.pdf, deriving the FRW metric, and I don't fully understand how the Ricci Vectors eq 8.5 can be attained from 7.16, by setting ##\partial_{0} \beta ## and ##\alpha=0## I see that any christoffel symbol with a ##0## vanish and so so do any...

What's the simplest, most direct way to derive the lagrangian of the SM? I saw earlier today: L[S M] = L[Dirac] + L[mass] + L[Gauge] + L[Gauge/psi] That seems like a good starting point. I like it because it says the SM Lagrangian is simply the sum of four lagrangians. The next step...

Please, can anyone explain me the steps made in the resolution of this integral? http://en.wikipedia.org/wiki/Common_integrals_in_quantum_field_theory#Yukawa_Potential:_The_Coulomb_potential_with_mass

Homework Statement Trying to derive the work and kinetic energy from principle ie ∫force⋅ds, for a pendulum, with θ at the vertical. Homework Equations ∫force⋅dx The Attempt at a Solution I toke the ∫mgsin(θ)⋅ds as the displacement and direction of the gravitation is opposite leading to the...

Homework Statement The velocity of a particle is related to its position by: v2 = w2 (A2 - x2) where w and A are constants. Show that the acceleration is given by: a=-w2x[/B]Homework EquationsThe Attempt at a Solution a= v* dv/dt v=(A2w2-x2w2)1/2 dv/dt= 1/2 (A2w2-x2w2)-1/2 * -2xw2 v *...

Where one can find a proof of the expectation value of operator expression. <A> = < Ψ | A | Ψ > or <A> = integral( Ψ* A Ψ dx ) Thanks.

Hello, I read a derivation for the width of the depletion region W in "SEMICONDUCTOR DEVICE FUNDAMENTALS" by Robert F. Pierret in which at one point it says: http://imageshack.com/i/ipbgKsK9p Here again for better readability: x_N = \sqrt{\frac{2 K_S...

Homework Statement The goal is to derive the heat equation with convection, ut=α2uxx-vux but for the case where u(x,t) instead models concentration changes by diffusion and convection. The idea is to use conservation of mass to do this. Homework Equations We are given: Change of mass inside...

Homework Statement Derive a mathematical relationship which encapsulates the principle of continuity in fluid flow. Homework EquationsThe Attempt at a Solution Imagine we have a mass of fluid ## M##, of volume ##V##, bounded by a surface ##S##. If we take a small element of this volume...

I've attached the part from Landau & Lifschitz Mechanics where I got confused. "The necessary condition for S(action) to have a minimum (extremum) is that these terms (called the first variation, or simply the variation, of the integral) should be zero. " Why is this a necessary condition? If...

Homework Statement given a medium in which p=0, j=0 but where the polarization vector P=P(r,t). Derive the wave equation satisfied by E and B.Homework Equations i started with the 4 basic Maxwells equations ∇ · D = ρ (1) ∇ · B = 0 (2) ∇ × E = −∂B/∂t (3) ∇ × H = J + ∂D/∂t (4) and with the...

Homework Statement Having one of those days where nothing makes sense, here is the derivation: how does he get the two circled terms from what he's derived above? Homework Equations N/A The Attempt at a Solution I tried substitution but get nowhere I just can't see how the early...

Homework Statement Given characteristic equation for a circuit containing a diode, I must figure out how to fit a polynomial to the curve so that the van der pol equation is obtained. The paper I am reading is here: http://www.unige.ch/math/hairer60/pres/pres_rentrop.pdf My doubts are...

Hello, I have encountered an equation in page 33 in the book of D.MacMahon titled QFT demystefied. It is the third equation from the top...how did the sum appear as a middle step of the equation? best regards. Abolaban

hello, i am trying to learn the derivation of the momentum operator and i found 2 ways of deriving it. one is using Fourier transform and the other is taking the time derivative of the expectation value of x. i just want to know what is the physical interpretation of the time rate of change...

My textbook says, basically, for an adiabatic process... All three variables in the ideal gas law—P, V, and T—change during an adiabatic process. Let’s imagine an adiabatic gas process involving an infinitesimal change in volume dV and an accompanying infinitesimal change in temperature dT. The...

In the book, 'Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics', the author, Laurent Nottale, makes a few interesting comments in the introduction of his book which seems a bit unclear to me. In the general introduction of the book, Nottale...

This is the solution to an exercise in Griffiths where one has to derive the Clausius Mosotti relationship: http://physicspages.com/2012/11/28/relation-between-polarizability-and-susceptibility/ I have one small question about the use of the word ''applied'' at the beginning when defining...

Homework Statement For a single molecule, derive the internal energy U = 3/2kBT In terms of the partition function Z, F = -kBTlnZ Where Z = V(aT)3/2 Homework Equations Thermodynamic identity: δF = -SδT - pδV p = kBT/V S = kB[ln(Z) + 3/2]The Attempt at a Solution U = F + TS δU = δF +...

In deriving thermodynamic temperature scale, it uses the concept that heat transfer between two reservoirs is the function of the reservoirs' temperatures. i.e. Q1/Q2=Φ(T1,T2). And then further express that Φ(T1,T2)=ψ(T1)/ψ(T2). I have two questions, 1. Is it a hidden assumption that the...

Sometimes when studying I'll run into a derivation that seems unclear, unmotivated, or which seems to require outside information. What do you do in those cases? Search online? Bang your head against the equations? Look for another book? I'm specifically asking about learning things on my own...

Okay so I'm using Coloumb's law and the defining equation of electric field strength to find a proof (for my own satisfaction) for the electric potential formula: V_A = \frac{PE_A}{q}= \frac{Q}{4πε_0r} (where A is the position configuration of a point charge q in an electric field) My derivation...

The derivation of the law have been put up in the forums but I have a question regarding its derivation. I understood everything from the assumptions to the application of Newton's Third Law, but I got stocked at this step: \frac{m}{k} = \frac{M}{k'} . This is similar to \frac{C}{M} =...

In the derivation on Wikipedia, it says the following ## \frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=\frac{dv}{dx}v = \frac{d}{dx}[\frac{v^2}{2}] ## How do they go from the second to last to last equation? I've been trying to understand, but I think I'm just looking over something incredibly simple.

I have been tearing my hair out for a while over a step in the proof of the relation pV^{\gamma}=constant. The textbook has assumed that we are dealing with an ideal gas undergoing an adiabatic process. Therefore dQ=0 and we get $$C_vdT + (c_p-c_V)\left(\frac{\partial T}{\partial...

I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being done in the radiation...

derivation of wiens displacement law and wiens distribution law from thermodynamic principle.but not from Plancks law

I'm a bit confused about how the work-energy theorem for a single particle can be extended into the general law of conservation of energy for the macroscopic system, particularly the point where we divide the kinetic energy of the system into macroscopic kinetic energy and internal kinetic...

http://en.wikipedia.org/wiki/Helmholtz_decomposition#Derivation how do we go from to also on the next step ∇' just means the gradient with respect to r', right? Also, why do i have to use the dirac delta function? i thought it was only used to deal with discontinuities? also when we say...

Taken from Steane's "Relativity made relatively easy" equation 4.8 I have been trying to show (4.8) using these relations earlier on in the book: Tried most means (rearranging, taking dot products) but can't seem to make it work. Is there an easy method I'm missing out?

Hi, I'm trying to get the relativistic kinetic energy, ## T ##, from the work expended, ## W ##, (assuming that the body is at rest initially) and I'm doing it like this (in 1D): \begin{equation} W = T = \int F ds = m \int \frac{d(\gamma u)}{dt}u dt = m\int u d(\gamma u) \end{equation} Where...

In SR the speed transformation formula (in response to a change of inertial frame of reference) is usually derived from the Lorentz transformation of space and time coordinates. I would like to find a direct derivation starting from the existence of a maximum speed limit (c) in respect to any...

Homework Statement Hi, I'm having trouble solving this problem: I can't seem to get to the right derived formula. The one selected is wrong. I'm still attempting to solve this. Homework Equations B= 8 M0 N (I - I0) 1251/2 a e = 2V m B2 R2 The Attempt at a Solution...

In class we went through the derivation of the energy of a perturbed system, I've dug my old notes out and found a bra ket derivation of the same thing, there's just one step that doesn't look right and was wondering if someone could tell me if its a misprint or actually correct (and why)...

Homework Statement 2. Find the formulae as in (3.4.1) for each of the following: (a) the rotation of angle π/2 about the point i ; Homework Equations The equation 3.4.1 is given below. ## f(z) → z*a + b ## where a, b and z are all complex numbersThe Attempt at a Solution I have attached my...

A Monatomic gas passes from state 1 (pressure p1, volume V1) to state 2 (p2, V2). Derive an expression for the change in entropy of a monatomic ideal gas. The required final equation is: ΔS = Cv ln(T2/T1) + nRln(V2/V1) In my attempt, I am retrieving ΔS = Cv ln(T2/T1) + Rln(V2/V1) i.e.; the...

Dear all, can you please verify if my derivation of the algebraic formula for the rotation isometry is correct. The handwritten file is attached. The derivation from the book (Alan F beardon, Algebra and Geometry) which is succinct but rather unclear is given below. Assume that f (z) = az + b...

Homework Statement The piston is initially at the top of the tube and the air pressure is equal to P0 (ambient pressure). After it is released and drops to location x, the pressure can be computed as follows. Assuming the air is an ideal gas with constant specific heats and assuming the process...

https://courses.physics.illinois.edu/phys406/Lecture_Notes/P406POM_Lecture_Notes/Derivation_of_the_Sabine_Equation.pdf I can't understand anything from the above link. Is there any alternative way to derive Sabine's formula. I searched in google but coundn't find anything.

Can somebody please tell me what should be present in the free body diagram for this system below. Also please mention the arrow details like which direction each force in the free diagram should be acting in. I really need to understand this concept...

I see that Planck scale of mass-energy is related to the corresponding length scale by application of the uncertainty principle. What is not clear for me is how we find either energy or length scale to compute the other one? What goes wrong if we assume a higher energy level than the Planck...

I am having some issues with the derivation of the Planck Radiation Formula, as for instance given in http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html . My point is that the assumption of cavity modes implies the formation of standing waves inside the cavity walls. In most situations in...

Homework Statement I need to derive this formula, and I'm basing it upon the following method (this has the diagram which I will be talking about below) http://isites.harvard.edu/fs/docs/icb.topic1214926.files/Purcell-appendix-B.pdf The Attempt at a Solution I'm fine with everything apart from...

Homework Statement Homework Equations au/as=T au/av=p S/R=ln[(v-b)(u+a/c)^2] The Attempt at a Solution 1/T=1/au/as=as/au S=ln[(v-b)(U+a/v)^2]R as/au=[(v-b)2(U+a/v)(1)]R/[(v-b)(U+a/v)^2]=2R/(U+a/v)=1/T T=(U+a/v)/2R U=2RT-a/v au/av=-P au=-Pav integrate au to get u=-pv+c u=-pv+c=2RT-a/v...