deriving Definition and 962 Threads

Hi all, I am trying to follow the calculation by samalkhaiat in this thread: https://www.physicsforums.com/threads/finding-equations-of-motion-from-the-stress-energy-tensor.547502/page-2 (post number 36). I am having some difficulty getting the equation above equation (11) (it was an unnumbered...

Homework Statement [/B] I'm trying to write a program in MATLAB which demonstrates a tautochrone curve and how the starting point of a ball is irrelevant as to the time it takes to get to the lowest point in the curve (without friction). At the moment I'm just trying to model it using a simple...

Hello, A little something I've been working on for fun today was trying to derive the rocket equation: Δv=V_{e}ln(R) So first I start with F=ma =m\frac{dv}{dt} \frac{F}{m}dt = dv ∫_{0}^{Tco} \frac{F}{m}dt = ∫_{0}^{v} dv Where Tco is the time of engine cutoff, and v is the velocity at that...

On the attached picture I have started trying to derive the path integral but I don't know how I get further. Can anyone help me? Also I have used that: exp(-iHΔt/ħ) = exp(-i(T+V)Δt/ħ) = exp(-iTΔt/ħ)exp(-iVΔt/ħ) But my book says that this identity is only correct to first order, i.e. there is...

I'm trying to derive a formula for the magnetic torque on a semicircular loop. what I've done so far is this The magnetic force on the non-curved loop is $\vec{F}_{x}=\int Idx\hat{i}\times B_{\circ}\hat{i}=0N$ for the curved loop $\vec{F}_{c}=\int_{0}^{\pi} Ird\phi\hat{\phi}\times...

Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested (oyc.yale.edu). Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...

How can I derive a contradiction from the following nasty statement: Assume $\sqrt{5} = a + b\sqrt[4]{2} + c\sqrt[4]{4} + d\sqrt[4]{8},$ with $a,b,c,d \in \mathbb{Q}$? *This is the last piece of an effort to prove that the polynomial $x^4-2$ is irreducible over $\mathbb{Q}(\sqrt{5}).$*

Homework Statement Let φ=φ(r) and r=√x2+y2+z2. Find ∂2φ/∂x2. Show that it can be written as (1/r + x2/r3)∂φ/∂r + x2/r2∂2φ/∂r2. Homework Equations Use the identity ∂r/∂x = x/r. The Attempt at a Solution I think I know ∂φ/∂x. Using the chain rule, it's ∂r/∂x ∂φ/∂r. That gives x/r ∂φ/∂r. If...

Homework Statement Given: Ideal gas equations: Find S(T,V) for an ideal gas Homework Equations Ideal gas equations: \begin{array}{l} {\rm{}}\\ U = \frac{3}{2}N{k_B}{\left( {\frac{N}{V}} \right)^{2/3}}\exp \left[ {\frac{S}{{\left( {3/2} \right)N{k_B}}} - {s_0}} \right]{\rm{ }}\\ T = {\left(...

... electron transport. 1. Homework Statement Electron - Phonon scattering, derive the contribution to electron transport. Homework Equations Trig. The Attempt at a Solution Am I being REALLY stupid here, I can't see how the equation matches the triangle. If you resolve KF' doesn't KF'...

Homework Statement Show that: ##B=\frac { 1 }{ 4\pi \epsilon r^{ 3 } } \left[ 3\hat { r } \left( \hat { r } \cdot \vec { m } \right) -\vec { m } \right] ## Homework Equations B=delxA, m=a*I The Attempt at a Solution [/B] I follow my professors derivation. However, she expands the term...

I'm looking at Carroll's lecture notes 1997, intro to GR. Equation 7.27 which is that he's argued the S metric up to the form ##ds^{2}=-(1+\frac{\mu}{r})dt^{2}+(1+\frac{\mu}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}## And argues that we expect to recover the weak limit as ##r \to \infty##. So he then...

In A. Zee "QFT in a nutshell" in chapter I.5 Exercise 1.5.1 on page 39 for spin 2 massive propagator. I know I’m missing something very simple (self-taught beginner). I'm trying to derive equation (13) on page 35, which is G_{\mu\nu,\lambda\sigma} = G_{\mu\lambda}G_{\nu\sigma} +...

Homework Statement Overall reaction: A + F = I + J (just take = as the equilibrium sign) It is first order in both A and B. The following mechanism has been proposed: 1. A + B = C + D 2. C + D = E + B (B is the catalyst) 3. E + F = G + H 4. G + H = I + J These are all...

Just one last question today if someone can help. I'm trying to derive the electromagnetic field strength tensor and having a little trouble with (i think) the use of identities, please see below: I understand the first part to get -Ei, but it's the second line of the next bit I don't...

Homework Statement derive the Fourier sine and cosine transforms of $$f(x) = e^{-cx}$$ by using $$e^{iax}=cos(ax)+isin(ax)$$ and computing the integral $$\int_0 ^{\infty} e^{-cx}e^{iax}dx$$.Homework EquationsThe Attempt at a Solution i'm completely clueless, all i did was evaluate what they...

So basically I was wondering whether it's possible to get the expression of ideal gas using molecular flux equation which is ##\phi = \frac{1}{4}\bar{v}n##. The derivation should be straightforward. I need to get the expression of pressure. Because the flux by definition already gives the rate...

Homework Statement Prove that ## [L_a,L_b] = i \hbar \epsilon_{abc} L_c ## using Einstein summation convention. I think I have achieved the solution but I am not sure of my last steps, since this is one of my first excersises using this convention. Homework Equations [/B] ## (1)...

I'm looking at Lecture Notes on General Relativity, Sean M. Carroll, deriving the FRW metric, and I'm a little confused with the use of eq 8.4 . I thought instead it should be using the general form of a spherically symmetric metric, not a vacuum spherical symmetric - eq 7.13 has been derived...

Homework Statement Hi my question is whether an SOP = POS for a given function F(A, B, C, D). Or is the SOP a complement of POS?Tasked to convert derive a simplfied SOP from a 4 var Kmap with don't cares. My answer was, F = C'.D' + A'.B'.C which is correct. Then for part B they asked for the...

Homework Statement Consider particles in a gas centrifuge. This device is used to separate gases of different molar mass by rotating a cylinder at high rates. Derive two equations: one for the pressure (P) and one for the particle number density (nv) as functions of M, r, w and T, where r is...

Hi dear forum members, I'm an undergrad. physics student(freshmen),i've learned that Galilei found g.t^2=s formula(a free falling object's position function with respect to time)without using physical foundations,by using him blood impulses for count time not utilizing acceleration etc,i've...

Homework Statement Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ Homework Equations x = Rcosθ y = Rsinθ The Attempt at a Solution Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2...

I am trying to derive the gravitational red shift effect but I think I am going about it all wrong. Specifically, I want to derive the change in frequency/ wavelength when a photon moves away from the surface of a star mass M and radius R. So I tried to use relativistic mass of the photon and I...

I am looking at derivations of the Doppler effect for sound and light, and I am very confused about what stays the same when it comes to sound. In this video, at 5:10, it is said that the wavelength will be the same. I'm not sure I agree with this because I'm pretty sure both the observed...

In Schwartz QFT book, while explaining the Faddeev-Popov procedure, he presents this following observation at (25.99): Can someone help understanding me why this expression equals one? THANK YOU!

Homework Statement A dog accelerates from 2.0 m/sec to 5.0 m/sec while covering a distance of 14.0 m. How long did this take Homework Equations d=(Vi+Vf/2)t The Attempt at a Solution 2(-Vi-Vf)d=t I am doing something wrong. Please help. Thanks[/B]

Homework Statement Using the Boltzmann distribution for a small system in contact with a heat reservoir at temperature T, find the Maxwell-Boltzmann distribution. Homework Equations The Boltzmann distribution states that the probability density of a system in contact with a heat reservoir at...

Can anybody out there show me how the sine wave formula y=Acos(kx - ωt + φ_{0}) or y=Acos(kx + ωt + φ_{0}) is the direct solution of the wave equation \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} ? I mean I looked it over on the Internet but everybody keeps...

I have a projectile that can only launch at 30 degrees and a target exactly 100m away at the same elevation on flat ground with 1g (9.8m/s2 meters per second per second?) What velocity without (then with) air resistance would the "muzzle velocity" need to be? (with a droplet shape for...

Hey I'm having an issue deriving the calculus of variations because the chain rule i use ends up different to the one in the textbook. Firstly I assume we have some function of 3 variables Y=y+alpha eta with grad Y'=y'+alpha eta' and x. Secondly we have an integral of this function over x and...

Hello there, I want learn to do homogenous differential equations and I cannot work out what is wrong in this example. Hope you'll be able to tell me why my DE is unsatisfactory. Assume that a capacitor is has charge Q and that the terminal with the high voltage is connected to a switch in...

1. Derive (∂U/∂P)V=-T(∂V/∂T)S 2. I must use dU=TdS-PdV 3. Derivations are my weakest part of math. I checked many wikis about Total differentials, partial derivatives, Maxwell relations and derivations. I can use the Thermodynamic Square, I know how to find different Maxwell relations but I am...

I am at the very last part of a relatively long derivation of the Casimir effect, and I just don't understand the final step D: So far, I have derived the ground state energy to be \langle 0| \hat{H} |0\rangle = \delta (0) \int _{-\infty}^{\infty} dp \frac{1}{2} E And for a massless field...

Hi guys, I was wondering if anyone knows of a good source/paper that I can find online that details how to derive the MSW Hamiltonian from a field-theoretic approach, or from an effective field theory approach or anything like that? Every time I study the MSW effect, the Hamiltonian...

Homework Statement Derive an equation for the change in free energy, ΔGmixing, when ideal gases with the same temperature and pressure, are mixed. Homework Equations ΔGmixing = nRT∑(xi)ln(xi) (∂/∂T(G/T))p = -H/(TxT) The Attempt at a Solution Pi = xiPi* μi = Gi,m μ = (∂G/∂n) at constant T...

Hi all, As a beginning theoretical chemist, I'm trying to understand how Tanabe-Sugano diagram was derived. Can someone help me understand the derivation in a nutshell? Thanks!

△Work = △KE + △PE Work = Force x Distance W=F△x Pressure = Force/Area W=PA△x Volume=Area x length W=PV Work = Pressure x Volume KE=(1/2)mv^2 Density = mass/volume mass = density x volume m=DV KE=(1/2)DVv^2 (work done by air pressure?) PE=mgy PE=DVgy (work done by gravity and air pressure??)...

I am sure this has a simple answer, but I don't seem to get it at the moment. I am going through a derivation of the Boltzmann's distribution by maximising the entropy with the constraints that the sum of the probabilities add to 1 and the average energy is some constant value. My question is...

Homework Statement Show that for a projectile d^2 (v^2)/dt^2 = 2g^2 Homework EquationsThe Attempt at a Solution Since we are only dealing with the y component for this. 2nd derivative would be 2. But since gravity acts on it then d^2 (v^2)/dt^2 = 2g. I don't get how to get to 2g^2. Can someone...

How does one derive the combined gas law rigorously from Boyle's Law, Charle's Law and Gay-Lussac's law? I started out as follows (I will be using ##P## for pressure, ##T## for absolute temperature, and ##V## for volume - for constants I will use subscripts to denote the parameter on which the...

Hi, I am trying to find an equation that would give the mechanical advantage of this system: I am fairly new to this kind of analysis, but my understanding is that to determine the MA I need to consider that: W_{in} = W_{out} F_{in} d_{in} = F_{out} d_{out} F_{out} / F_{in} = d_{in} /...

Homework Statement A gun can fire an artillery shell with a speed v_0 in any direction. Show that a shell can strike any target within the surface given by: (gr)^2 = (v_0)^4 - (2gz)*(v_0)^2 where z is height and r is horizontal distance the target is from the gun. Homework Equations Some...

I'm trying to find the azimuthal angle unit vector \vec{\phi} in the cartesian basis by taking the cross product of the radial and \vec{z} unit vectors. \vec{z} \times \vec{r} = <0, 0, 1> \times <sin(\theta)cos(\phi), sin(\theta)sin(\phi), cos(\theta)> = <-sin(\theta)sin(\phi)...

How to derive the formula: v=wr where v is the tangential velocity, w is the rotational velocity, and r i the radius vector? From the attached image, it can be concluded that (each quantity is a vector): w=r x v, also v=w x r, and r= v x w. All three vectors are perpendicular to each other...

Is it possible to derive the speed of light from quantum electrodynamics (like it can be done from Maxwell's equations) or is the fact that the speed of light in vacuum is constant and has a certain value an assumption in the theory? My understanding is that QED assign a mass zero to photons and...

I'm a bit confused about the derivation of the Schwarzschild radius. I can do it quite easily using Newton's Law of gravitation, but this law is only an approximation, so I am wondering whether the result I obtain, r_{s}=\frac{2GM}{c^{2}}, is an approximation or not. It seems to me that it...

Homework Statement I have a problem where the circuit is as follows: (pic attached I hope) but if you can't see it it's just a power source (AC), resistor and inductor with 2 terminals across the inductor (from were you measure the voltage). I want to derive the response function, and I am...

In the attachment I have used the derivation of the wave equation with a slight modification to derive the diff equation that when solved gives the time independent schrødinger equation. Since I have dome this myself I am worried that this might be totally wrong or a bit wrong. Could someone...

For a vector : ##\nabla_a V^b=\partial _a V^b+T^b_{ac}V^c## I am trying to derive for a covector: ##\nabla_a w_b=\partial _a w_b+T^c_{ab}w_c## I am told to use the Leibniz Rule and the definition that for a scalar ##f## : ##\nabla_a f =\partial_a f ## to do so My thoughts: Define ##w_b##...