Derive Definition and 620 Threads

Tong proposes the following exercise in this lecture (around 25:30, section b)): Exercise statement: Prove that the stress-energy tensor is given by the functional derivative of the action with respect to ##\delta g^{\mu \nu}## $$T_{\mu \nu} = \frac{-2}{\sqrt{-g}} \frac{\delta S}{\delta...

In my textbook, the effective force of a particle on a rotating frame is given as below: The diagram is: What I do not understand is the expression for Rf dotdot, which is given as below: According to the book, an arbitary vector Q can be expressed as: So Rdotdot w.r.t fixed frame can be...

where ##A## is a constant.

Here is the diagram of the problem: and here is the answer of the question: What I don't understand is equation 1 and 2. The Hook's law states that F = -k(change in x) Why the change in x1 equals to x1-x2+l? x1-x2 equals to the length of the compressed spring. I cannot convince myself that...

Can someone tell or lead me to how we derive this forumla I=nqAv for current?

I am a student minor in physics and I am taking this course of particle physics. And I have been lost since the Non-Abelian Gauge Theory which a few lectures before Electroweak unified Theory lecture. i am completely confused and overwhelmed by the math since the mid-term exam, since I was not...

Firstly, this is not a homework question. I found a worksheet online with an example of a square law circuit built using log-antilog operational amplifiers. I tried to derive the transfer function but I can't seem to eliminate the reverse saturation current term ##I_S##. I would really...

I am trying to figure out the total energy a system of falling buckets can produce, and whether it would be a system that can replace or enhance a system of turbines in a hydroelectric dam situation. I need to figure out the total energy that a system of buckets, suspended on a chain system...

This image shows the equations. I managed to almost get equation 5, but my partial derivative is not squared but instead multiplied by mu, and also I don't have a factor of 1/2. Here is an image of the work I have. I'm sorry for any sloppiness. I tried to be as concise as possible when writing...

There are more parts to this problem but I can't get to those until I finish this one. I have attached figure.1 and some my work so far, including my answer which the system rejected. (I had to copy my work from my original sheet as it contained sensitive information I didn't want to upload)...

Dear all. I'm learning about the discrete Fourier transform. ##I(\nu) \equiv \int_{-\infty}^{\infty} i(t) e^{2 \pi \nu i t} d t=\frac{N}{T} \sum_{\ell=-\infty}^{\infty} \delta\left(\nu-\ell \frac{N}{T}\right)## this ##i(t)## is comb function ##i(t)=\sum_{k=-\infty}^{\infty}...

I'd first like to preface this post with the "right answer" per wikipedia (I've seen the same answer elsewhere on more reputable websites) The thing I find trouble some is the cross terms such as ##n_2 \cos \theta_i## where indices of refraction are "mixed with the other angle". I have...

Where can I find a reference to a derivation of Born's rule for arbitrary observables from Bohmian mechanics?

I know that for normalized quaternion, $$\hat{q}$$, the derivative is given by $$\frac{d\hat{q}}{dt}=\frac{1}{2}\hat{q}\cdot \omega$$ where $$\cdot$$ denotes the quaternion multiplication. I want to calculate the time derivative of a non-normalized quaternion q. I tried to calculate the...

You may be familiar with how you can express a vector field as a linear combination of basis vectors like so: X = Xi∂i Now, I know that normally, the basis vectors ∂i can be derived by taking the derivatives of the position vector for the coordinate system with respect to all the axes like...

So far the best I've been able to come up with is to use ##\vec{B} = \mu_0 \vec{H}## which gives me i_c = H 2\pi r j_c = \frac{H 2\pi r}{\pi r^2} = \frac{2H}{r} \therefore B = \mu_0 \frac{r j_c}{2} I'm fairly confident this is just terrible math and physics on my behalf but I'm struggling to...

So the other day, I was pouring beer from a can to a mug and I obviously know the flow rate depends on the height of the beer from the bottom of the can (fluid level in the vessel), angle of tilt and I think time as well. I was wondering how to best model the PDE to describe such a phenomenon (...

Summary: QED describes all physics under certain energy level. So how we derive results that we know from QM from QED? I want to know how to get quantum mechanics from QED (Quantum Electrodynamics). In QED we showed that the potential between two electrons goes like 1/r as in quantum...

Hi If 2 signals of frequencies y1 = A cos ##\omega_1## t and y2 = A cos ##\omega_2## t are combined the resultant signal is given by y = y1 + y2 y = 2A cos (w1-w2)t/2 cos (w1+w2)t/2 If w1~w2 then one can plot the beat phenomenon from this equation. But if w1 >> w2 as in the...

Attempt: $$\nabla \times ( a\nabla b) = \epsilon_{ijk}\frac{\partial}{\partial x_j}(a\frac{\partial b}{\partial x_k})\hat e_i$$ $$ = \epsilon_{ijk}\big(\frac{\partial a}{\partial x_j}\frac{\partial b}{\partial x_k}+a\frac{\partial b}{\partial x_j\partial x_k}\big)\hat e_i$$ $$= \nabla a \times...

I am not sure where does the dy term, phi^2 and phi^4 terms come from. I guess there are dx and dy because we have to account for the nearest neighbour pairs in the x and y axis? I guess there is a phi^2 term because 2q_a*q_b=(q_a-q_b)^2-q_a^2-q_b^2, the term q_a^2-q_b^2? How about the phi^4 term?

Firstly, I don't know in which Picture this equation holds (if I hadn't missed some words in the previous text...). I think it may be the Heisenberg Picture. But if it is, the rest target is to prove $$\frac{i}{\hbar}[H_R+H_{FR},(a^\dagger) ^ma^nO_A]=\langle\frac{d}{dt}((a^\dagger)...

If anyone has read Hamilton's Lectures on Quaternions, lines 13 and 15 of Section 563 (p. 566) have successfully resisted my efforts for months. For those interested, I can provide the Latex version. Let me also apologize if this is the wrong forum for the question. Thanks.

##P(T=1|W=w)=\frac{P(\{T=1\}\cap\{W=w\})}{P(W=w)}=\frac{\binom {n-2} {w-1} p^{w-1}(1-p)^{(n-2)-(w-1)}}{\binom n w p^w (1-p)^{n-w}}=\frac{(n-2)!}{(w-1)!(n-w-1)!}\frac{w!(n-w)!}{n!}\frac{1}{p(1-p)}=\frac{w(n-w)}{n(n-1)}(p(1-p))^{-1}##. I cannot seem to get the terms with ##p## out of my expression.

I began by taking E = mc^2 and E = hf , where h is Planck's constant, and then rewrote E as 1/2mv^2. I rewrote f as c / λ, which made hf become h*c / λ. I then set this expression equal to the Kinetic Energy equation 1/2mv^2, which gave me: 1/2mv^2 = h*c / λ I then replaced c on the...

Hi all, How to derive the energy of a parabolic confining potential in a wire as shown below? I tried to follow the derivation of the harmonic, oscillator like we did for the quantum well and the magnetic field but i can't find anything that has an expression that come close to the one shown...

Hello I need to derive this equation from Grittfith's quantum book $$ \frac{d^2y}{dr^2} = r^2y$$ I know I can use the characteristic equation: $$m^2 = r^2 \rightarrow y = e^{r^2}$$ but the answer should be: $$y=Ae^{\frac{-r^2}{2}} + Be^{\frac{r^2}{2}}$$ I know from Euler's formula that...

I know I can get momentum in terms of kinetic energy in this way: K = .5mv^2 => p = sqrt(2mK) substitute into debroigles gives me: λ = h/(sqrt(2mk)) = hc/(sqrt(2mc^2K)) which would be the nonreletivistic equation but I need the reletivistic equation. I can plug in the equation for...

I'm having trouble understanding a specific line in my lecturers notes about the path integral approach to deriving the Klein Gordon propagator. I've attached the notes as an image to this post. In particular my main issue comes with (6.9). I can see that at some point he integrates over x to...

I tried following: $$ \Delta l = \alpha l_0 \Delta T $$ $$ (\Delta l)^2 l_0 = \alpha l_0^2 \Delta T \Delta l $$ $$ \Delta A l_0 = \alpha A_0 \Delta T $$ $$ \Delta A = \frac{ \alpha A_0 \Delta T }{ l_0 } $$ If we remember that: $$ \Delta l = \alpha l_0 \Delta T $$ So we have $$ \Delta A = \frac{...

Homework Statement I'd like to derive the equations of motion for a system with Lagrange density $$\mathcal{L}= \frac{1}{2}\partial_\mu\phi\partial^\mu\phi,$$ for ##\phi:\mathcal{M}\to \mathbb{R}## a real scalar field. Homework Equations $$\frac{\partial...

hello, I am trying (and failing) to verify / derive the result of the Legendre polynomial P11 (cos x) = sin x Griffiths Quantum chapter 4 Table 4.2 I figured it would not be too bad. I have attempted this 3 or 4 times trying to be careful. I keep getting sin(x) times some additional trig...

Let ##Q_ik## be a symetric tensor, so that ##Q_ik= \frac{m}{2} \dot x_i \dot x_j + \frac{k}{2} x_i x_j## (here k is also a sub, couldn't do it better with LaTeX). How do we derive such a tensor, with respect to time? And what could such a tensor mean in a physical sense? It really looks like the...

Homework Statement The Gibbs-Thompson relation provides a correlation between solubility and radius of curvature. Consider two spherical particles of radius r and R present in a solvent, with R >> r. The rate of dissolution of the smaller particles (the rate of decrease in its radius with time)...

How to derive Nielsen equation from Lagrange equation

Homework Statement Two masses m1 and m2 are joined by a spring of spring constant k. Show that the frequency of vibration of these masses along the line connecting them is ω = √[ k(m1 + m2) / (m1*m2) ] (Hint: Center of mass remains at rest.) Homework Equations f = w/2π w = √(k/m) F = -kx a = -...

Homework Statement Derive the expressions for the voltage gain (Gv) of the following op amp: Homework Equations In = Ip = 0 Vp =VnThe Attempt at a Solution I can use KCL, and the fact that In and Ip are both 0, to derive the two equations, one from the top node and the other from the...

Homework Statement You need to derive a formula for undamped pendulum simple harmonic motion; 1. Starting from the middle point 2. Starting from the extreme point Homework Equations The solutions are; 1. s = s0 sin(2 pi f t) 2. s = s0 cos(2 pi f t) The Attempt at a Solution I can derive the...

Is there any source that how can I derive the Malus of ? Where there's two polarizer This is the equation $$I_{out}=I_{in}[H_{90}+(H_0-H_{90})]cos^2(θ)$$ ##H_0=1/2(k_1^2+k_2^2)## and ##H_{90} = k_1k_2## Also I need to derive the $$I_{out}=1/2I_{in}cos^2θ$$ using integrals Please help

I put the level for this thread as I, but anything from B to A is acceptable here. I'm hoping this isn't too imprecise, but what are the easiest or simplest (or fastest) ways to derive the Lorentz transformation equations you know? I am not after blatant corner cutting here, by the way. Just...

Hey guys! How do I derive the general expression for delta p times delta x which is the exception value in the harmonic oscillator. I am supposed to establish delta p and delta x as operators and the express those operators by raising and lowering operators.

Homework Statement Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong. Homework...

Homework Statement The table gives the theoretical relative intensities in LS-coupling for all possible ##^3F – ^3G## transitions. a) Use this data to verify the sum rules for LS-intensities in a multiplet. b) Use the sum rules to derive the relative intensities in a ##^2D – ^2F##...

I've been able to derive the centripetal & transverse accelerations, and I understand how the radius of curvature is the reciprocal of the curvature, and that to get the radial & Coriolis acceleration, I need to get the time derivatives of the radius of curvature, but I don't see exactly how...

(apologies for re-posting, I am unable to find my original thread.) A material which has a Young's modulus of elasticity of 250 GN m-2 and a poisons ratio of 0.32, calculate: (a) the bulk modulus of the material 
 Relevant equation, K=E/3(1-2v) Inputting our known values...

here is a link with the formula: https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms.pdf i'm talking about the formula that says the integral of f'(x)/f(x)dx = ln(f(x))+C it's kind of hard to put this into Google. where does this formula...

Homework Statement For a single mechanical unit lung, assume that the relationship among pressure, volume, and number of moles of ideal gas in the ling is given by PA((VL)/(NL)a = K, where a = 1 and K is a constant. Derive the lowest-order (linear approximation to the relationship among changes...

I am planning to derive analytically the transconductance transfer function (Iout/Vin) of this Gm2.sch circuit block. Is my small-signal model for Gm2.sch correct ?There is one minor mistake (Vgs5 should not be zero). Could anyone spot other mistakes in the small-signal circuit ? I am planning...

Hi there. I am trying to derive Gauss's law from the divergence. I would like to know if it is correct: The divergence is defined as (I saw this on Fuller & Byron "Mathematics of classical and quantum physics") ##...

How can I derive mathematically law of composition of velocities from time dilation and length contraction But please use only algebra .Don't use four vectors and space time diagrams.