Derivation Definition and 1000 Threads

Hi this is my first post the forum, nice to meet you all. I am trying to derive the time dilation formula following the image attached. However I am unsure of the algebra being used toget from the 2nd line of working to the 3rd line. Can someone please tell me what the name of the algebra...

I have to derive the Lorentz time transformation given the equation for gamma and the equation for the Lorentz space transformation. I started by using relevant equations from the Space derivation done in class (also the one that Ramamurti Shankar does). Here is a picture of what I have tried...

The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...

This question stems from one of the recent homework threads. I'm familiar with the derivation given here regarding mass accretion and ejection, where the general idea is to define a system around body and all of the incoming/leaving mass so that we can once again apply NII to the whole thing. I...

on page 269 it's written in the second edition of Schutz's textbook that ##(10.69)p_c/\rho_c=\beta (2-5\beta)^{-1}##. Demanding that this be less than ##1/7## gives: ##(10.70) 0<\beta < 1/6## Now, if I am not mistaken on page 268 in equation (10.57) the condition should be ##p_c/\rho_c >1/7##...

Hello everyone, I'm stuck doing this problem, I've tackled the partial derivative but i can't figure out the derive for x component part, i solved the partial derivative part, i came to this result: What do can i do from here on, thank you!

V=ir considering the whole circuit Now we knowV=E-ir Then ir=E-ir Therefore i=E/2r Therefore,V=E/2

My thought is following: However this would give me w=E_m + E_n instead of E_m-E_n I guess something relating to hermiticity or adjointing something has gnoe wrong in my version. Can someone point me in the right direction please? :) Thank you in advance!

x = fraction of potentiometer connected to load Vp in parrallel with VL = x/(Rp/RL.x.(1-x) + 1) If RL = infinite, then Ro = x and Vo = x.Vs If RL = finite, then Ro = x/(Rp/RL.x.(1-x) + 1) and Vo = x.Vs/(Rp/RL.x.(1-x) + 1) Therefore error is x.Vs - x.Vs/(Rp/RL.x.(1-x) + 1) Trying to break the...

hi guys our solid state professor gave us a series of power point slides that contains the derivation of Bloch theorem , but some points is not clear to me , and when i asked him his answer was also not clear : in the first part i understand the he represented both the potential energy and the...

My work is in the following pdf file:

Hi guys I saw that equation of the velocity of electrons In a periodic potential $$ v = (1/h) grad E(k) $$ in my textbook we use in our solid state physics course without any proof or any thing and when I searched for it I found that its derived in Ashcroft book appendix E : Is there is any...

My attempt at solution is in the HW template, though this is not an HW question.

I am trying to understand the following derivation in my lecture notes. Given an n-dimensional manifold ##M## and a parametrized curve ##\gamma : (-\epsilon, \epsilon) \rightarrow M : t \mapsto \gamma(t)##, with ##\gamma(0) = \mathbf{P} \in M##. Also define an arbitrary (dummy) scalar field...

Hello, Here in this thread I will derive formulas for relation between two wheels, either teethed (e.g. gears) or non-teethed. In wheel relationship, we have three cases: Two wheels at the same axle Two wheels intersected in parallel (meshed) Two wheels connected by a belt We will examine...

Hello all, In high school physics, the magnitude sum of vector addition can be found by cosine rule: $$\vec {R^2} = \vec {F^2_1} + \vec {F^2_2} + 2 \cdot \vec F_1 \cdot \vec F_2 \cdot cos ~ \alpha$$ and its angle are calculated by sine rule: $$\frac {\vec R} {sin ~ \alpha} = \frac {\vec F_1}...

I wanted to make a derivation of the Lorentz transformation : $$x'=Ax+Bt\\t'=Dx+Et$$ The conservation of the quadratic form ##c^2t'^2-x'^2## yields the equations: $$A^2-B^2/c^2=1\\D^2-E^2/c^2=-1/c^2\\AD=BE/c^2$$ Hence ##B=c\sqrt{E^2-1}##,##D=\sqrt{E^2-1}/c##,##A=\pm E##. The speed of the...

They write on page 618: where for those who don't have the book at hand, I'll write the related equations: $$(18.94) \ \ \ \sigma(e^+ e^- \to \text{hadrons})=\frac{4\pi \alpha^2}{s} [ I am c^1(q^2)+Im c^{\bar{q}q}(q^2) \langle 0| m\bar{q}q|0\rangle+ $$ $$+Im c^{F^2}(q^2)\langle 0 |...

i was trying to derive the Vdc in a fullwave rectifier with smoothing capacitor , i guess i had it right as my final equation matches the book equation : Vdc~(1-(1/2fRC))Vp , but i am not really sure that my attempt was completely right as i assumed that Vdc is the average value of the...

Hello, In second-order derivative test, the test is inconclusive when ##f''(c)=0##, so we had to generalize to higher-order derivative test. I was wondering how such tests can be generalized and derived? For example, how can I prove that ##f(x)=x^4## have minimum at 0? Bagas

Hello, In high school, I had been taught about finding substitution resistance from Wheatstone bridge. The formula: a. If the cross product of ##R1## and ##R3## is same as ##R2## and ##R4##, the galvanometer in the middle (##R_5##) can be omitted and use series-parallel principle to solve for...

Summary:: This is a system and we want to find the equations of motion. After some force-based attempts, I think that it would be easier to use some energy methods. Hi, I wanted to ask about deriving equations of motion by using the Lagrangian. The question is in the picture below. We are...

Hi, I just wanted to ask a question about the derivation of the stream function \psi for a doublet. In the pictures below is a derivation (in this one the source is on the left and the sink is on the right). I understand everything in the left photo, however my questions are: 1) Why do we...

Just started learning about uniform circular motion. I really don't understand how we get aΔt2/2 on the side. I also searched on the internet for a similar derivation, but there are none so simple. Thanks for your help! P.S There is a mistake in calculation in second line (textbook error).

Not sure how they obtained an answer of (2meukenetic *Mg/R^2)*r^2 dr = dt When they say disk I am assuming it's not ring shaped. So since F * Dr= DT where I guess F acting on a small point on the disc is constant from the table top. And Dr is the variable distance from a random small point from...

Imagine that we have an electromagnetic wave or light propagating in x direction, and \mathbf{E} is oscillating in z direction and \mathbf{B} in y direction. The picture looks something like this Now, if there exists a charged particle q on the xx axis at rest, then our B field can't do...

In this derivation,i am not sure why the second derivative of the vector ## S_j '' ## is equal to ## R^{u_j}{}_{xyz} s^y_j v^z y^x## could anyone explain this bit to me thank you it seems ## S_j '' ## is just the "ordinary derivative" part but it is not actually equal to ## R^{u_j}{}_{xyz}...

The speed of sound in a gas at temperature T is given to be ## v=\sqrt{\frac{\gamma RT}{M}}##, where ##\gamma## is the adiabatic exponent, R is the gas constant and M is the molar mass of the gas. In deriving this expression, we assumed that the compression and expansion processes were so fast...

The integral is called the line integral of ##F## from ##A## to ##B##. The work done in the displacement by the force is defined as, ##W(A\rightarrow B)=\int_A^B \vec{F}.dr## where the limits ##A## and ##B## stand for the positions ##r_A## and ##r_B##. We now return to the free particle...

I understand the derivation of T= 2π√m/k is a= -kx/m, in a mass spring system horizonatally on a smooth plane, as this equated to the general equation of acceleration of simple harmonic motion , a= - 4π^2 (1/T^2) x but surely when in a vertical system , taking downwards as -ve, ma = kx - mg...

To arrive at the Robertson-Walker metric for a spatially homogeneous and isotropic cosmology, one first writes down the the metric for spatial sections i.e. constant t surfaces, dσ2 = d2 +f2(r) (dθ2 + sin2θ dφ2), where f(r) can take only 3 special forms, and then one promptly writes the...

Summary: This equation is used in ISO standard ISO 6336-6. I want to understand how it is derived. This equation helps to consolidate damage caused by multiple torque, cycle bins. A bin means a torque applied for a given number of cycle. As an outcome of the equation, a single equivalent...

Twice I found the following derivation of ##E\propto v^2## in a little distinct forms. https://www.physicsforums.com/threads/the-final-explanation-to-why-kinetic-energy-is-proportional-to-velocity-squared.78484/#post-609992 The derivation is in post #9, if it is not shown properly. This...

When deriving ##\Pi(\vec{x},t)## for the Klein-Gordon equation (i.e. plugging ##\Pi(\vec{x},t)## into the Heisenberg equation of motion for the scalar field Hamiltonian), we come across a term that is the following ##\int_{-\infty}^{\infty}d^{3}y...

For undamped free vibrations, we have the following differential equation. mu'' + ku = 0 where m is the mass of the object hanging on the end of a spring, and u is the distance from the equilibrium position as a function of time. This yields u = Acosωt + Bsinωt where ω is √(k/m)...

dG= -SdT + VdP ... now dividing by dV holding temperature constant (dG/dV)T = -S (dT/dV)T + V (dP/dV)T ... now dT and constant temperature cancel out final answer: (dG/dV)T = V (dP/dV)T

In his book, Landau derives the Lorentz transformations using the invariance of the interval, and I have some questions about it that I would like to clarify 1. What is a parallel displacement of a coordinate system? Does it refer to moving along any axis? I don't see how any arbitrary...

Homework Statement: I don't know how can I derivation Eq.(2.2) Homework Equations: Fourier coefficients Homework Statement: I don't know how can I derivation Eq.(2.2) Homework Equations: Fourier coefficients Dear all. I don't know how can I derivation Eq.(2.2). Where Σk is come from??

On page 238 of his second edition of Schutz's he writes the following: Where Eq. (9.107) is: $$\bar{h}^{TT}_{xx}=A\cos (\Omega (z-t)) , \bar{h}_{yy}^{TT}=-\bar{h}^{TT}_{xx}$$ and ##\delta \bar{h}^{TT}_{xx}=2\pi \sigma m \Omega \ell_0 R \sin [\Omega (z-t)-\phi]##. Here's what I tried: $$A\tan...

I want to derive from ##T^{\mu \nu}_{,\nu}=0## the equation: ##\int T_{0\mu}d^3 y=constant##, I don't see how exactly. From the derivative I know that ##T^{0\mu}_{,\mu}=0##, but I don't see how to integrate this equation, it's ##T^{00}_0+T^{0i}_i=0##. But how to proceed from here? Thanks in...

I'll write down my calculations, and I would like if someone can point me to my mistakes. $$\partial_t \int T^{00}(x^i x_i)^2 d^3 x = -\int T^{0k}_{,k}(x^i x_i)^2 d^3 x = \Dcancelto[0]{-\int (T^{0k}(x_ix^i)^2)_{,k}d^3 x} +\int (T^{0k}(x_i x^i)^2_{,k})d^3 x$$ After that: $$\partial_t \int...

This is such a small point but I just wondered if anyone could clarify. It is easy to work out the time between successive collisions with one wall of the box, namely $$\Delta t = 2L/v_{x}$$However, if this time interval is for instance 1 second, then we could have either 1 or 2 collisions in...

I have a little question about converting Velocity formula that is derived as, ##\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}## in Cartesian Coordinate Systems ##(x, y, z)##. I want to convert this into Polar Coordinate System ##(r, \theta)##...

Hello everyone, I am stuck in the derivation of the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is$$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term using...

Is it possible to derive escape velocity say using momentum and force balance considerations? or using angular momentum consideration? Namely, any other approach then energy consideration that utilizes gravitation potential energy and kinetic energy?

According to Schutz's second edition book, the equation for Riemann tensor to first order in ##h_{\mu\nu}## is: $$R_{\alpha\beta\mu\nu}= \frac{1}{2}(h_{\alpha \nu,\beta \mu}+h_{\beta\mu,\alpha\nu}-h_{\alpha\mu,\beta \nu}-h_{\beta \nu , \alpha \mu})$$ which (as stated in the book) can be derived...

Homework Statement: The homework problem is included below, but I am looking at the derivatives of vectors. Homework Equations: I have the properties of derivatives below, but not sure they help me here...