Relation Definition and 1000 Threads

Hi all, I've been able to find the answers to most of my questions in these forums, but this time I was not able to. So here goes my first post: I've been learning about thin film interference, and it all makes sense to me except for the correlation between destructive interference caused by...

Are there fundamental limits on the accuracy for measuring both position ##q## at time ##t## and momentum ##p## at time ##t+\Delta t##, with tiny ##\Delta t##? If yes, why? If no, why can't one then measure (in principle) both ##q## and ##p## arbitrarily well at the same time ##p## (which is...

My professor informally defined a n-ary relation as a "function" that assigns to an n-tuple from arbitrary sets ##X_1, X_2, ... X_n## a well-formed statement that either holds or does not hold. I know that this definition is somewhat informal, but how can the professor use the word function if...

Hi all, I read in Cheng and Li's book "Gauge theory of elementary particle physics" Ch 11, specifically : Eq. (11.46) that the hypercharge commutes with the SU(2) generators, i.e., ##[Q-T_3,T_i]=0##, I'd like to understand what that mean and how this could be proved ?

$\tiny{{s4}.{13}.{5}.{41}}$ $\textsf{find if planes are $\parallel, \perp$ or $\angle$ of intersection }\\$ \begin{align} \displaystyle {P_1}&={x+z=1}\\ \therefore n_1&=\langle 1,0,1 \rangle\\ \\ {P_2}&={y+z=1}\\ \therefore n_2&=\langle 0,1,1 \rangle\\ \\ \cos(\theta)&= \frac{n_1\cdot...

Hi all! Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice): $$cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 +...

can anyone help me ? i have a homework and i did't find any answer for it the question is find the Domain , Range , matrix and the digraph for the relation R a ) A = { 1,2,3,4,8 } = B , aRb if and only if a=b b) A = { 1,2,3,4,6 } =B , aRb if and only if a multiple of b

Homework Statement At first I needed to calculate the angular resolution of a telescope (diameter 1m, for visible light) so I used θ=1.22λ/D and got 4.88x10^-7 rad. Now I am asked: "If we wished to use this telescope to image the moon, what is the closest distance two objects can be to be...

I have a really simple question that I can't figure it out. I have a process X that took 905 seconds to finish. Process Y took 950 seconds to finish. I want to know a) how much in % process X is faster than Y, and b) how much in % process Y is slower than X? I think that the answer is the...

Homework Statement Which cannot be the structure of two acoustic branches, nor three acoustic branches? Simple cubic, FCC, BCC, diamond cubic, NaCl lattice Homework Equations N/A http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61...

Below is a snipet from http://file:///C:/Users/Christian.Hollersen/Downloads/Britto_2011_2%20(1).pdf of Britto. Similar explanation can be found in the QFT books of Zee, Schwarz or the Scattering Amplitude text of Huang. Or any other text that covers BCFW recursion. My dumb question: how and...

Homework Statement Find a recurrence relation for the number of ternary strings of length n that contain two consecutive 0s. Homework EquationsThe Attempt at a Solution Let ##a_n## count the number of ternary stings of length n that contain two consecutive 0s. Then, we can split the total...

Homework Statement If ##a_n## counts the number of ways to climb a flight of n stairs if one can take 1, 2, or 3 steps at a time, then ##a_n = a_{n-1} + a_{n-2} + a_{n-3}##. What are the three initial conditions? Homework EquationsThe Attempt at a Solution I would say that ##a_0 = 1## since...

Homework Statement Homework Equations I don't think there are any in this case The Attempt at a Solution I know that in order to prove R is an equivalence relation, I'd have to show that it is Reflexive, Symmetric, and Transitive. I'm not sure why, but I'm finding this a bit difficult in...

I am a little confused about how we prove that a solution for a recurrence relation is correct. For example, say that I have the recurrence relation ##H_n = 2H_{n-1} +1##. Using an iterative process, we guess that the solution is ##2^n - 1##. Now, to prove that this is correct, it seems that it...

Hi there, Suppose we had a car going in a circle. We know that the turning angle(angle between the movement direction and the wheel axis) and the friction are connected, because friction determines the centripetal force and it determines the radius of the circle that we make with our car. I need...

Homework Statement Deduece the commutation relations of position operator (squared) \hat R^2 with angular momentum \hat L Homework Equations [xi,xj]=0, Lj= εijkxjPk, [xi, Pl]=ih, [xi,Lj]=iℏϵijkxk The Attempt at a Solution The previous question related R and L and the result was [\hat R,\hat...

Homework Statement Suppose you are given the following relation among the entropy S, volume V , internal energy U, and number of particles N of a thermodynamic system, where A is a constant.: $$ S = A(NVU)^{\frac 1 3} $$ Find the chemical potential μ(T,P) Homework Equations $$ \frac μ T =...

I've just started with statistical mechanics and arrived at the part where they relate entropy to the number of microstates for a given system. The derivation starts of by adding an amount of heat ##\delta Q## to a system and observing the resulting change in internal energy : $$\delta U =...

Homework Statement A gas obeys the equation of statez=1/(1-b(molar density)) What is the molar entropy change of expanding this gas from a volume of 1 dm3 to 2 dm3 at a temperature of 300 K, given b = 0.2 dm3? Calculate your answer to three significant figures and select one answer from the...

Hey! :o Let $f(x)=x^3-3x-1\in \mathbb{Q}[x]$. Then $f(x+1)=(x+1)^3-3(x+1)-1=x^3+3x^2+3x+1-3x-3-1=x^3+3x^2-3$. The prime $p=3$ divides all the coefficients except of the one of the term of the highest degree and $p^2$ doesn't divide the constant term. So, from Eisenstein's criterion we...

can dark matter explain Tully-Fisher relation, or is modified MONDlike gravity a better explanation for this? new paper The Radial Acceleration Relation in Rotationally Supported Galaxies Stacy McGaugh, Federico Lelli, Jim Schombert (Submitted on 19 Sep 2016) We report a correlation between...

Homework Statement I have the following circuit What is the relation between $$I_{eq}~~and~~ i_1, i_2, i_3$$? Homework Equations Kirchhoff Laws The Attempt at a Solution See the image above

Hello all. I have a question about a reflexive relation. Consider ##1_V : V \rightarrow V## with ##V## a vector space. Obviously, this is an isomorphism. My book uses this example to show that V is isomorphic with V (reflexive relationship). However, suppose I have a function ##f: V\rightarrow...

Recently, I was thinking about the nature of reciprocity in some cases of natural phenomenon, for example, Newtons Thrid Law of Motion, or, Faraday's Law of Induction. Considering that spacetime distortion, due to a gravity field, leads to a change in the light path, or, a change in light...

Here's a thought from other thread A reply So what's the relation between gravity and the laws of thermodynamic, or should it be conservation of energy?

We know that Poincare matrix which is 0 Kx Ky Kz ( -Kx 0 Jz -Jy ) describes the boost and rotation is very similar to -Ky -Jz 0 Jx...

With a modest understanding of 'spooky action at a distance', I've been informed that using entangled particles as a form of quantum bit system would not work for vast distances. It wouldn't be a viable option to communicate instantly with points like our moon, satellites orbiting Jupiter, or...

Suppose you are given a first order system whose transfer function is HP(s) = KP/(TP*s + 1). Now, you want to control this system using a standard P (proportional) controller whose transfer function is HR(s) = KR (a proportionality coefficient). There is also disturbance that acts upon this...

Homework Statement I want to prove this relation ##J_{n-1}(x) + J_{n+1}(x)=\frac{2n}{x}J_{n}(x))## from the generating function. The same question was asked in this page with solution. http://www.edaboard.com/thread47250.html My problem is the part with comparing the coefficient. I don't...

Dear all, in a lot of undergraduate textbooks you find the claim that antiparticles can be motivated by Einstein's energy-momentum relation ## E^2 = p^2 + m^2 ##, which has both 'negative' and 'positive energy' solutions. In the context of a single wave function this is problematic. In the...

The definition from the current Wikipedia article is a good start: My technical question is whether "each further term" is a function of only the values of the preceeding terms, or is it also a function of the index of the "further term"? For example, if we are given that the values of two...

Homework Statement Homework EquationsThe Attempt at a Solution If I consider a specific case of adiabatic process , then ##dQ = 0 ## and ##dU = -PdV ## If we differentiate with respect to T on both sides , ##\frac{dU}{dT} = -P\frac{dV}{dT}## . Now , the closest I see is option B) , but...

KE is proportional to v^2. In a gravitational field KE=1/2 m*v^2. It's easy to find mathematically Work=Fd=mad=m(v/t)(v*t)=m*v^2. But how to visualize it or get an intuitively "feel" for this v^2 relationship?

So I see them in the books labelled as accoustic and optical phonons but I don't seem to find a comprehensive treatment of the matter for a beginner who doesn't know a thing about the dispersion curves. I'd prefer not to dwell too much into the mechanical treatment if possible since I just need...

I have a hard time understanding the variation of mass with velocity, more precisely the proof. In almost every material I've found, the author analyses 2 bodies colliding. The idea of looking at the collision is not hard to grasp and by considering one of the velocities equal zero, you get a...

You can model the probability for radioactive decay as a Poisson distribution. This is the probability for radioactive decay within a specific time interval. (I probably got some of it wrong here). P(k,μ)=λ^k⋅exp(-μ)/k! Is there a way to use this formula to derive the other formula for...

I derived a relation between the product of two linear polynomials and the square of their average. It can be used to solve any quadratic equation. Will this help me getting into a top university?

Hello everyone, I was wondering if anyone knows what the completeness relation for the fundamental representation of SO(N) is. For example, in the SU(N) we know that, if T^a_{ij} are the generators of the fundamental representation then we have the following relation $$...

Homework Statement The electric field and the electric potential at a point are E and V respectively. (a) If E=0, V must be 0 (b) If V=0, E must be 0 (c) If E≠0, V cannot be 0 (d) If V≠0, E cannot be 0 Homework Equations [/B] E = V/d The Attempt at a Solution [/B] I basically substituted...

Hi folks, Let's pick a simple example, the H atom. We can calculate all spherical armonics, all quantum numbers so we are able to know which are all the possible states of the electron. We know all the values this observables can take. But the question is, let's say we have a handbook of...

Find the relationship between $X$ and $Y$ if $$X= 1 + \frac{2}{1!}- \frac{2^3}{3!}+ \frac{2^5}{5!}- \frac{2^7}{7!}+\cdots ...$$ and $$Y= 2-\frac{4}{3!}+\frac{6}{5!}-\frac{8}{7!}+\frac{10}{9!}-\cdots ...$$

Given the positive real numbers $a,\,b,\,c$ and $x,\,y,\,z$ satisfy the condition $a+x=b+y=c+z=1$ Prove that $$\left(abc+xyz\right)\left(\frac{1}{ay}+\frac{1}{bz}+\frac{1}{cx}\right)\ge 3$$.

I have a question regarding the two seemingly different phenomenon of gravity and entropy.I want to ask that exactly how the gravity and over-all entropy of the universe are related?The thing that came to my mind is that could gravity be not a fundamental force of nature at all? Could it be a...

Hi All, I have a little query concerning the derivation of PV γ = constant. In my textbook of Physics, first they give the equation for adiabatic process using the first law of Thermodynamics, as; dEint = W → (1) where, ΔEint ⇒ change in internal energy and W ⇒ workdone Then, they used...

As far as I know, in most of metals, IR radiation is reflected almost entirely and is not absorbed by metals. How does a metal become warmed under IR radiation? or does reflection, on its own, can warm up a metal?

Hi everyone! I am new to mechanical engineering and recently I started about compressors. I am trying to find relation between torque, speed and output efficiency of the compressor. Can anyone help me with simple explanation so that I can understand. I will be really thankful if you could help...

So, I know that according to everything online water pressure is independent from everything except gravity, height, and density of fluid. The situation I'm talking about is slight different. Imagine a standard water bottle that angles inwards near the top. Now imagine a point on the side of...

Hello, as a non-physicist enthusiast, but with decent math background, I tried to learn a bit about origins of quantum theory and very soon raised some questions, which I hope this community will answer. So, Planck tried to model the blackbody radiation on where Raighley and Jeans have failed...

Hello, I'm trying to calculate a recurrence relation of the phases of 3 telescopes in a closure phase. Usually in a stellar interferometer we have 3 telescopes, located in a triangle, measuring intensity of light in 3 points on a far field plane. I found an article, describing how the phase is...