Theorem Definition and 1000 Threads

Hi. My question is about nucleon-nucleon scattering. In David Tong's lecture note, he discusses Wick's theorem and nucleon scattering (page 58-60). My problem is that I don't know how to calculate the second line of eq(3.48): \begin{equation} <p'_1, p'_2|:\psi^\dagger (x_1) \psi (x_1)...

Hello! Recently I found this article: http://quantum-journal.org/papers/q-2017-07-14-13/pdf/ Being familiar with some basis of quantum formalism, I, nevertheless, experienced several difficulties with understanding of the theorem described in this paper. I would really appreciate if someone...

In his book: Introduction to Real Analysis, Manfred Stoll does not prove parts (a) and (b) of Theorem 2.2.6 on the limits to certain special sequences ... I am having trouble getting started on the proof of part (a) ... can someone please help me to make a meaningful start to the proof ...

Homework Statement consider a ski jumper moving down a track to acquire sufficient speed to accomplish the ski jumping task. The length of the track is L=25m and the track makes an angle of 45° with the horizontal if the skier starts at the top of the track with zero initial speed , determine...

Question: A) Derive the work - energy theorem for one particle. B) Check whether it is applicable for a system of particles and a rigid bodyWork - energy theorem for one particle system, total sum of work done by individual forces = work done by total force To show the above equality, let's...

I was thinking about why the buoyant force on an object should depend solely on it's volume and not shape. It seems loosely like the divergence theorem in that an integral over the surface is determined by the volume. There is a big difference though; in the divergence theorem we integrate...

Find product (1+3i)(2-2i) then change each to complex form and find product with DeMoivres theorem clueless!

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with Theorem 2.1.45 concerning the Supremum Property (AoC), the Archimedean Property, and the Nested Intervals Theorem ... ...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with an aspect of the proof of Theorem 2.1.38 ... Theorem 2.1.38 reads as...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Section 1.4: Entry 2: Axioms for the Integers ... In this section Bloch defines the integers as an ordered integral domain that satisfies the Well Ordering Principle ... rather than defining the...

So here's the question: You are given that F is a conservative vector field, except for singularities at the points (0,1), (2,0), (3,0), and (0,4). You are given the following information about line integrals around the following closed paths: 1) Around the curve C1 given by x^2 + y^2 = 2...

Hi, Our lecturer explained us the Reynold Transport theorem, its derivation , but I don't get where the - sign in control surface 1 comes from? He said that the Area goes in opposite direction compared with this system. I can't visualise this on our picture. Can you please help me understand...

1. Homework Statement Attached: Homework Equations I've just changed the notation a tad to make things quicker for me : ##\phi_1=\phi_1(x_1)## and ##\Phi_2=\phi_2(x_2)## : denotes normal product. i.e annhilator operators are on the RHS, so acting on a vacuum state will give zero. I can...

This is the problem I'm currently working on: The pi groups I identified were h1, h2, d, D, g, t, and velocity, but when I looked at the solution, it selected Δh, D, t, ρ, d, ϒ, h1, with no explanation why those variables are needed. If I was solving with the Bernoulli equation, I wouldn't...

Hello! I have been doing a previous exam task involving the divergence theorem, but there is a minor detail in the answer which i can't fully understand. I have a figur given by ${x}^{2} +{y}^{2} -{z}^{2} = 1$ , $z= 0$ and $z=\sqrt{3}$ As i have understood this is a hyperboloid going from...

Hello everybody. I have to prove the fallowing theorem: The Cayley-Hamilton Theorem help me please...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.2.9 (6) ... Theorem 1.2.9 reads as follows: In the above proof of (6) we read the...

Charles Link submitted a new PF Insights post An Integral Result from Parseval's Theorem Continue reading the Original PF Insights Post.

Hello, today i was playing around with the pythagorean theorem and found out something that i can't really explaing or atleast explain it with probably a false answer. So i was putting every possible combination with the max digit of 10. For example 1^2+1^2=\sqrt{2}, 1^2+2^2=\sqrt{5}...

Hello, It is me again.So i was watching some math videos and i came across Fermat's Last Theorem which was very intersting.But i was confused because i wondered for a second and sayed "well if A,B and C are equal then they could be 0 to prove it" but at the same time i thought "well if it works...

Consider a continuous function f in [a,b] and f(a) < f(b). Suppose that \forall s \neq t in [a,b], f(s) \neq f(t). Proof that f is strictly increasing function in [a,b]. Homework Equations I.V.T: If f is continuous in [a,b] and \gamma is a real in [f(a),f(b)], then there'll be at least one c...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 47: Galois Groups... ... I need some help with an aspect of the proof of Theorem 47.1 ... Theorem 47.1 and its proof read as follows: At the end of the above proof by Anderson and Feil, we...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 47: Galois Groups... ... I need some help with an aspect of the proof of Theorem 47.1 ... Theorem 47.1 and its proof read as follows: At the end of the above proof by Anderson and Feil, we...

Homework Statement Question attached: Homework Equations [/B] Using the result from two fields that ## T(\phi(x) \phi(y))= : \phi(x) \phi(y) : + G(x-y)## Where ##G(x-y) = [\phi(x)^+,\phi(y)^-] ## ## : ## denotes normal ordered and ##\phi(x)^+ ## is the annihilation operator part , and...

This proof is taken from this site: http://cmt.dur.ac.uk/sjc/thesis_ppr/node12.html I get that ##v_{ext}(r)## and ##N## determines ##H## from proof 1. But why is ##\Psi## determined by ##H##? Can someone derive a path to prove it mathematically?

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 45: The Splitting Field ... ... I need some help with an aspect of the proof of Theorem 45.6 ... Theorem 45.6 and its proof read as follows: https://www.physicsforums.com/attachments/6701At...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 45: The Splitting Field ... ... I need some help with an aspect of the proof of Theorem 45.6 ... Theorem 45.6 and its proof read as follows: At the start of the proof of Theorem 45.6 we read...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 45: The Splitting Field ... ... I need some help with some aspects of the proof of Theorem 45.5 ... Theorem 45.5 and its proof read as follows: In the above text from Anderson and Feil we...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 45: The Splitting Field ... ... I need some help with some aspects of the proof of Theorem 45.5 ... Theorem 45.5 and its proof read as follows: In the above text from Anderson and Feil we...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 45: The Splitting Field ... ... I need some help with some aspects of the proof of Theorem 45.4 ... Theorem 45.4 and its proof read as follows: My questions on the above proof are as...

I am reading Anderson and Feil - A First Course in Abstract Algebra. I am currently focused on Ch. 45: The Splitting Field ... ... I need some help with some aspects of the proof of Theorem 45.4 ... Theorem 45.4 and its proof read as follows: My questions on the above proof are as...

This is out of Jackson's electrodynamics, problem 1.15. I am trying to prove the theorem that if a number of surfaces are fixed in position and a given total charge is placed on each surface, then the electrostatic energy in the region bounded by the surfaces is an absolute minimum when the...

Hello! Why do the singularities in the Residue Theorem must be isolated? If we have let's say a disk around ##z_0##, ##D_{[z_0,R]}## where all the points are singularities for a function ##f:G \to C## with the disk in region G, but f is holomorphic in ##G-D_{[z_0,R]}##, we can still write f as a...

Homework Statement Hi guys, I have the following transmitted power signal: $$x(t)=\alpha_m \ cos[2\pi(f_c+f_m)t+\phi_m],$$ where: ##\alpha_m=constant, \ \ f_c,f_m: frequencies, \ \ \theta_m: initial \ phase.## The multipath channel is: $$h(t)=\sum_{l=1}^L \sqrt{g_l} \ \delta(t-\tau_l).$$...

Determine if the triangle with the given vertices is a right triangle. (7, -1), (-3, 5), (-12, -10) I must find the lengths of the sides using the distance formula for points on the xy-plane. The question then tells me to use the converse of the Pythagorean theorem. How do I use this...

The Weinberg-Witten theorem (https://en.wikipedia.org/wiki/Weinberg–Witten_theorem) states that A ##3 + 1##D QFT quantum field theory with a conserved ##4##-vector current ##J^\mu## which is Poincaré covariant does not admit massless particles with helicity ##|h| > 1/2##. A ##3 + 1##D QFT...

Hello! I came across Jordan Curve Theorem while reading something on Complex Analysis. I don't know much about topology and I apologize if my questions is silly, but from what I understand the theorem states that a closed curve in the complex plane separate the plane into an inner region and an...

Hello! I am reading a book on complex analysis and I came across this: If ##G \in \mathbb{C}## is a region, a function f is holomorphic in G and ##\gamma## is a piecewise smooth path with ##\gamma \sim_G 0## then ##\int_\gamma f = 0##. I want to make sure I understand. First of all, ##\gamma...

This weekend I was trying to calculate the work-energy theorem, considering a body that can be treated like a particle, and has its mass varying in time. I searched through a lot of sites if such thing existed, and didn´t find anything. Then I found a thread...

Hi All, According to the fundamental theorem of algebra: "every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots". My question is: what about polynomials with degree say 2.3 or 3.02, as in the polynomial: ## p(x) =...

Hello. Uh, I'm trying to undestand how to prove Thevenin's theorem. The Sadiku book puts an independent current source where the load used to be in order to reach the equation: V = Vth + I*Rth. I do understand how he reaches that conclusion after putting the source, what I don't understand is...

Hi. I'm not a physicist, but I’m intrigued by Bell's theorem and I've been stumbling with "superdeterminism." My understanding of the concept is that everything is not just predetermined, but the initial conditions of the universe are fine-tuned and "conspire" so choices of which versions of...

[Mentor's note: This thread has was forked off from another thread because it was a digression there. This is false. Bell's theorem is based on a certain assumption (the statistical independence or free-will assumption). Some local and realistic theories that contradict this assumption exist...

I've managed to derive the form of Reynolds transport theorem as a bilance of linear momentum of the system: \left (\frac{\vec{\mathrm{d} p}}{\mathrm{d} \tau} \right )_{system}=\frac{\mathrm{d} }{\mathrm{d} x}(\int_{V}^{ }\vec{v}\cdot \rho dV)+\int_{A}^{ }\vec{a}dm+\int_{A}^{ }\vec{v}\cdot \rho...

Homework Statement F(x,y,z)=4x i - 2y^2 j +z^2 k S is the cylinder x^2+y^2<=4, The plane 0<=z<=6-x-y Find the flux of F Homework Equations The Attempt at a Solution What is the difference after if I change the equation to inequality? For example : x^2+y^2<=4, z=0 x^2+y^2<=4 , z=6-x-y...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with yet another aspect of the proof of Theorem 7.1.10 ...Theorem 7.1.10, and its proof, reads as follows...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with another aspect of the proof of Theorem 7.1.10 ...Theorem 7.1.10, and its proof, reads as...

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with another aspect of the proof of Theorem 7.1.10 ...Theorem 7.1.10, and its proof, reads as follows: In the proof of the above...

Homework Statement Using the power series for ln(x + 1) and the Estimation Theorem for the Alternating Series, we conclude that the least number of terms in the series needed to approximate ln 2 with error < 3/1000 is: (i) 333 (ii) 534 (iii) 100 (iv) 9 (v) 201 Homework Equations ln(x+1) =...

Homework Statement Are the groups ##\mathbb{Z}_8 \times \mathbb{Z}_{10} \times \mathbb{Z}_{24}## and ##\mathbb{Z}_4 \times \mathbb{Z}_{12} \times \mathbb{Z}_{40}## isomorphic? Why or why not? Homework EquationsThe Attempt at a Solution I think I am misunderstanding the Theorem of Finitely...