Derivation Definition and 1000 Threads

For this, Does someone please know how do we derive equation 9.9 from 9.8? Do we take the limits as t approach's zero for both sides? Why not take limit as momentum goes to zero? Many thanks!

I am trying to Derive Malus's Law. My textbook says that an electric field as an amplitude ##E## before passing thought the polarizer and reduce to ##E_{trans} = E\cos\theta##. I am trying to understand why this occurs my considering a vertically polarized light passing though a polarizer that...

Dear Forum, I have a question about the derivation of the Fermi golden rule in Kenneth Krane's Introduction to Nuclear Physics. I understand everything up to equation 9.20. However, it is unclear how he goes directly to equation 9.21. Here is equation 9.20, ## d\lambda =...

Dose someone please know why they have the absolute value bars in this derivation? many thanks!

For this, I don't understand how they got from (1) to (2)? Dose someone please know what binary operation allows for that? I also don't understand how they algebraically got from line (2) to (3). Many thanks!

I'm reading a book called Asymptotic Methods and Perturbation Theory, and I came across a derivation that I just couldn't follow. Maybe its simple and I am missing something. Equation 3.3.3b below. y(x) takes the form A(x)*(x-x0)^α and A(x) is expanded in a taylor series.

I am trying to solve Problem 2.4 in Ballentine: I note in my attempt below to what (2.6) and (2.7) refer. My attempt thus far is as follows: A ##2 \times 2## state operator can be represented in a particular orthonormal ##\beta = \{\phi_i\}## as below, where we have enforced trace...

This is the part of Schwinger-Dyson equations derivation. I did not understand how can we obtain the commutator in the last line of the picture. I understand why the delta functions appeared from Heaviside functions but there is no minus sign in any term so how can we get the commutator...

Hello, I am going over the derivation for two-electron density. I am having a hard time understanding how the second term in 2.11a seen below is derived. I know this term must eliminate the i=j products but can't seem to understand how. Thanks for the help.

Hello, I am trying and failing to derive that the shear modulus ##G## is equal to the Lame parameter ##\mu##. I start with the linear, symmetric, isotropic stress-strain formula: $$\sigma = \lambda \mathrm{tr}(\epsilon) \mathrm{I} + 2\mu \epsilon$$ I then substitute a simple (symmetric) shear...

TL;DR Summary: I want to find a function with f'>0, f''<0 and takes the values 2, 2^2, 2^3, 2^4,..., 2^n Hello everyone. A professor explained the St. Petersburgh paradox in class and the concept of utility function U used to explain why someone won't play a betting game with an infinite...

Hey, I am looking for a derivation of time-dilatation or some trivially equivalent formulas (Lorentz-transformation, conservation of 4-distance (edit: invariance of spacetime interval) etc) in 1 dimension, using that c is observer independent. I only can find the one that uses a light-clock...

I don't understand how they got from the previous step to the next step of the derivation circled in red: Many thanks!

In the derivation of the conservation law of the conservation of mass, the flux on one side enters and the flux on the other side leaves the control volume. I presume this is due to the assumption that the volume is infinitesimally small and hence v(x,y,z,t) will not change directions...

I want to follow the Lienard-Wiechert potential derivation in Robert Wald's E-M book, page 179. I do not understand $$dX(t_\text{ret})/dt$$ on the right side. I assume the chain rule is applied, but I can't see how. $$ \frac{\partial[x'^i - X^i(t - |\mathbf x - \mathbf x'|/c)]}{\partial x'^j} =...

In Section 3.4 of Shapiro & Teukolsky (1983), a simple derivation, due to Landau, of the maximum mass limit for white dwarfs and neutron stars is given. I will briefly describe it here and then pose my question. The basic method is to derive an expression for the total energy (excluding rest...

F= V dm/dt = V (dm/dx)(dx/dt) = V^2 (dm/dx) Fdx = V^2 dm E = m v^2. ,mass flowing with constant velocity If velocity is changing rather than mass, then E = 1/2 m V^2 Ok, joking aside, what is the best derivation of E= mc^2 ?

Could anyone help with some of the later parts of the derivation for Dirac spinors, please? I understand that an arbitrary vector ##\vec v## $$ \begin{bmatrix} x \\ y \\ z \end{bmatrix} $$ can be defined as an equivalent matrix V with the components $$ \begin{bmatrix} z & x - iy \\ x + iy...

In Compton's 1923 paper on X-rays scattering from light elements, he presents the following diagram: Here, ## h\nu_0/c ## is the momentum of the incident photon, ## h\nu_\theta/c ## is that of the scattered photon and ## mv/(1-\beta^2)^{1/2} ## is that of the recoiled electron. He uses this to...

This is a question on Einstein's 1907 paper first discussing equivalence principle and uniform acceleration. Picture a rigid accelerating object of length £ with a clock at each end. The rear accelerates for time τ (measured by the clock there) at a proper acceleration γ. The clock at the front...

I am trying to understand how one derives the dilaton monopole interaction. In "Black holes and membranes in higher-dimensional theories with dilaton fields", Gibbons and Maeda mentioned that one could obtain the dilaton monopole interaction as such: where the action is given by However, I...

Hi, Everyone! This is the page(first image) from Principle of physics by resnik. I want to ask the definition of work(##W=F(x) \Delta x##) by variable force here is somewhat different from the usual integral version. I don't understand how is this valid definition? Secondly, how did they reach...

Many texts state that in an elliptic orbit you can find angular momentum magnitude as $$ L = r m v = m r^2 \frac {d \theta} {dt} $$ I wonder if $$ v = r \frac {d \theta} {dt} $$ is valid at every point. I understand this approximation in a circumference or radius r but what about an arc...

One of the common derivations of the canonical ensemble goes as follows: Assume there is a system of interest in the contact with heat reservoir which together form an isolated system. Heat can be exchanged between the system and reservoir until thermal equilibrium is established and both are...

Boltzmann entropy definition is given by: $$ S = k_B lnW $$ where ##W## is the weight of the configuration which has the maximum number of microstates. This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...

Author computed ##f_{X_k}(x)## as follows but I don't understand it. Would any member explain me the following computations?

How did Voigt derive the average shear modulus of an anisotropic material, G=1/5 (A-B+3C), where 3A=c11+c22+c33, 3B=c12+c13+c23, 3C=c44+c55+c66? The original text is published in German about 100 years ago. I looked for other papers explaining this, but none has explained the derivation. They...

I know the formulas for perihelion and aphelion distances in an orbit with SMA a and eccentricity e are a(1-e) and a(1+e), respectively. However, why is this? I can't seem to find any derivations for this anywhere and also cannot figure this out myself.

This problem is from Griffiths' book Introduction to Electrodynamics [Problem 2.53 in 4th edition]. It considers that electrons are emitted from the cathode and move to the anode. This establishes a constant current between the parallel plates. It asks to show that the constant current ##I##...

I am having trouble understanding this derivation and need some guidance. 1) I tried solving the algebra from the first equation to the second equation circled in red. Can someone please help with what algebra steps, I cannot solve to the circled solution. 2) What does Ee stand for? Is it...

The magnetic flux ##\phi_m = \int{BdA}## The magnetic field of the coaxial cable B = ##\frac{I_{enc} \mu_0}{2\pi r}## since surface area of a cylinder = ##2\pi rdr L, dA = 2\pi L dr## where L is the length of the coaxial cable so ##\phi_m = \int{\frac{I_{enc} \mu_0}{2\pi r}2\pi L dr}##?

##\phi_m = Blwcos\theta## voltage = ##\frac{-d\phi_m}{dt} = Blwsin\theta\frac{d\theta}{dt}## where l is the length of the loop and w is the width of the loop The top and bottom of the loop have magnetic forces perpendicular to the loop. My book says that means that there is no current through...

Hello, I'm reading Group Theory in a nutshell for physicist by A Zee. When he introduced Dual tensors (pp 192), he made a claim with a light hint, and I have had great trouble deriving this claim, any help would be appreciated - Let ##R \in SO(N)## be an ##N##-dimensional rotation, then the...

Hello! Can someone point me towards a derivation (whether with Fermi Golden rule, or full QFT calculations) of the decay rate for the neutrinoless double beta decay: $$\Gamma_{\beta\beta}^{0\nu} = G^{0\nu}|M^{0\nu}|^2<m_{\beta\beta}>^2$$ Thank you!

McCabe - Thiele method is used to find minimum number of separation stages or theoretical plates for a given efficiency of separation in distillation for two - component mixture if components have similar enthalpy of vaporization. If components have similar enthalpy of vaporization ,than on...

Moderator's note: Spin-off from previous thread due to topic change. Because it doesn't work. Bohmian time evolution doesn't involve the coarse graining steps that are used in his calculation. A delta distribution remains a delta distribution at all times and does not decay into ##|\Psi|^2##.

Hi everyone, In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions about his derivation. 1) As a first step, he rewrites the correlation function as $$...

I need help with a derivation of an equation given in a journal paper. My question is related to the third paragraph of this paper: https://doi.org/10.1007/BF00619826. Although it is about fibre coupling my problem is purely mathematical. It is about solving a complex double integral. The...

https://www.researchgate.net/publication/301874096_Emergent_behavior_in_active_colloids/link/5730bb3608ae08415e6a7c0a/download (expression 9 on this document derivation). I understand the need for substitution etc into the integral. What puzzles me is how the integral equals what it does. If...

Queries regarding MKS to CGS system for the following formulas. Force - Newton (MKS), Dynes (CGS) Work - Joule (MKS), Ergs (CGS) 1N = 10^5 dynes. 1J = 10^7 ergs. How the above unit conversion formulas are derived ?

If you've seen it, they chose one point in the combustion chamber and the other in the exhaust nozzle. I think they're assuming that we have a gas both places. They say that the pressure in the nozzle is atmospheric pressure, or it you're in outer space, zero. That makes perfect sense...

Hi all, I am currently reading Bardeen's Paper on The Four Laws of Black Hole Thermodynamics: https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-31/issue-2/The-four-laws-of-black-hole-mechanics/cmp/1103858973.pdf and am struggling with the derivation of equation 26...

https://scholar.harvard.edu/files/schwartz/files/7-ensembles.pdf https://mcgreevy.physics.ucsd.edu/s12/lecture-notes/chapter06.pdf On page 3 of both the notes above, the author merely claims that $$P \propto \Omega_{\text{reservoir}}$$ But isn't $$P \propto...

The classical definition to the Kinetic Energy equation is KE=integral of F*dx where F=d(m*v)/dt. When mass is constant, KE=(1/2)m*v^2. I am working on a vibration problem at work and having to review my Lagrangian Dynamics books from 30 years ago. So my question is about all of the authors...

when the net force is constant then Q1. rate of change of momentum (dp/dt) is zero or constant Q2. assuming dp/dt is constant we replaced it with ----> p2-p1(total change in momentum ) ? how?

This is a spring problem From this, it says I need to answer in terms of kinematic friction which to me doesn't make much sense. I also looked at similar questions online to the "in terms of" problems and they don't use all four variables in their derived equation. Do I not need to use all...

The classical wave equation in 1-D reads: $$\frac{\partial^2 u}{\partial x^2}(x,t) = \frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}(x,t)$$ The D'alembert solution to the wave equation is: $$u(x,t) = f(x+vt) + g(x-vt)$$ so a allowed wave function solution to the 1-Dimensional classical wave...

Dear PF, so we know that cross product of two vectors can be permutated like this: ## \vec{ \alpha } \times \vec{ \beta }=-\vec{ \alpha} \times \vec{ \beta} ## But in a specific case, like ## \vec{p} \times \vec{A} = \frac{ \hbar }{ i } \vec{ \nabla } \times \vec{A} ## the cyclic permutation of...

Work - Energy principle states that work of resultant force or sum of work of all forces acting on some system equals change in kinetic energy of the system. For inviscid fluid flowing in a pipe such theorem can be used to derive Bernoulli's equation because as fluid flows it is subjected to...

I want to ask several questions regarding to the text: 1) Why do we find the minima of the diffraction? Why not the maxima?2) "Figure 25.32b shows two rays that represent the propagation of two wavelets: one from the top edge of the slit and one from exactly halfway down" Why do we take point...