Relation Definition and 1000 Threads

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 ...

Hi Have a look at this formula: Cv=((39.693*D^4)/K)^0.5 It correlates Discharge Coefficient (Cv) for a valve with Headloss coefficient (K) of the valve. Please explain this formula and let me know: 1- Is K fixed for a valve in every situations of it? 2- Assume an area of a valve is changed...

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...

As far as I understand it, the non-zero vacuum energy attributed to a quantum field (at each point in space-time) is precisely due to the Heisenberg uncertainty principle (and the fact that the energy of the quantum field at each space-time point is quantised). Accordingly (in order to satisfy...

Hi! Well, I'm programming a vehicle's physics, and I have trouble finding a way to calculate Rolling resistance, though i searched a lot. I already have the Traction Force and the Drag Force, but now I need Rolling Resistance. The best thing i found is that Froll = Croll * P, where Croll is the...

The magnetic moment ##\vec{M}## of a charged particle is defined as ##\vec{M}=\frac{1}{2}q\,(\,\vec{r}\times\vec{v})##. Starting with torque ##\vec{N}=\vec{M}\times\vec{B}##, I arrive at a contradiction. Consider a charge particle moving at a constant speed ##v## anticlockwise in a circle of...

I am wondering if it's possible for a relation to intercept with both it's derivative and indefinite integral at the same location (not including e^x as it shares the same rule as both it's integral and derivative). This is also assuming the constant of the indefinite integral is equal to zero...

Homework Statement What is the electric field strength at the position of the proton in the figure?(Figure 1) Assume that B = 0.10 T and F = 3.4×10−13N . Figure 1: https://session.masteringphysics.com/problemAsset/1385081/6/35.P29.jpg Homework Equations Honestly I don't know. Since we have a...

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under rotations, but not under boosts). Equivalenty, if one starts off with Minkowski spacetime from the...

We define a function T : \Bbb{N} -> \Bbb{N}, such that T(2k+1) = 2k+2 and T(2k) =k. Also, T^2(n)=T(T(n)), and generally: T^k(n)={T}^{k-1}(T(n)). a) Prove that for every n\in\Bbb{N}, there exists a positive integer k, such that T^k(n)=1 b) We say {c}_{k} is the number of elements in the set...

This is something I've been curious for some time. I've heard that there is a relation between gravitational waves and black holes. Moreover, this year the quite important paper "Observation of Gravitational Waves from a Binary Black Hole Merger" was published. Now, I'm starting to study...

Homework Statement Find a tight upper bound for the recurrence relation using a recursion tree argument Homework Equations T(n)=T(n/2)+T(n/3)+c The Attempt at a Solution I don't know how to do this problem because the tree doesn't have symmetry. One side of the tree can keep going because of...

I have a hypothetical question. If there was a relatively Earth-like planet out there that somehow experienced a rather catastrophic meteor impact large enough to alter its axial tilt close to 0 degrees, would such an event render the planet essentially a desert world? I.e. there are no more...

Homework Statement Let ##u## and ##v## be differentiable functions of ##x,~y## and ##z##. Show that a necessary and sufficient condition that ##u## and ##v## are functionally related by the equation ##F(u,v)=0## is that ##\vec \nabla u \times \vec \nabla v= \vec 0## Homework Equations (Not...

Hi, I have transmission line with dispersion relation ω=sin(kx), so then means that for one value of ω I have two values of k. I apply voltage with some frequency with is allowed to move in the line. First question is, how can I influence what k will be generated inside the line. The another...

Homework Statement Prove the following relation for ##\zeta:=r e^{i \theta}##: S(\zeta)^\dagger a S(\zeta)= a \cosh r - a^\dagger e^{i \theta} \sinh r with ##S(\zeta)=e^{1/2[\zeta^\ast a^2-\zeta(a^\dagger)^2]}## and ##a## being the annihilation operator with eigenvalue ##\alpha##...

hi every one can you tell me how to calculate the absorption coefficient of a thin film using the absorption and the transmittance spectrum plotted as a function of the wavelength (knowing that i don't know the thickness of the film )

Hi, I have been given a relation between stress and strain which is strain=(stress/70000)(1+(3stress/(1890)) the dia of round bar is 10mm and length is 3mm and that's all the data i have and I am required to find out permanent set.

Let A= {1,2,3}. Let R= {<1,1>,<2,2>}. I(A) (Identity Realtion) on A >(def)> {<x,x>|x \in A} So that mean : \forall <x,x> x \in A (That how I understood it) My question: Is R is identity relation on A ? Thank you !

Why is ##a_{ji}dG_j'=dG_i'## ? from the third last line below. ##G_i=a_{ji}G_j'## because a vector labelled by the space axes is related to the same vector labelled by the body axes via a rotation transformation. If ##a_{ji}dG_j'=dG_i'##, then we are saying a vector ##dG'## labelled by the...

The function ei(p.r – Et) is the central player in non-relativistic QM. Yet the expression (p.r – Et) is the Minkowski inner product of the space-time four-vector, (t,r), and the four-momentum (E,p) and as such is Lorentz invariant. According to Feynman, De Broglie realized the relativistic...

Homework Statement Consider a particle with mass m oscillates in a simple harmonic potential with frequency ω. The position, x, and momentum operator, p, of the particle can be expressed in terms of the annihilation and creation operator (a and a† respectively): x = (ħ/2mω)^0.5 * (a† + a) p =...

The equation following (3.80) seems to suggest that the velocity vector ##\vec{\dot{r}}## must always be parallel to the position vector ##\vec{r}##. But clearly this is not true as a particle's velocity can be in any direction. What's wrong?

Homework Statement Show that the scatter angles of the photon (θ) and electron (Φ) in the Compton effect are related by the relation: ##cot (θ/2 )=(1+\frac{hf}{mοC^2}) tan(Φ) ## Where f is the frequency of incident photon 2. The attempt at a solution I wrote down the equations of conservation...

Homework Statement Prove that isomorphism is an equivalence relation on groups. Homework Equations Need to prove reflexivity, symmetry, and transitivity for equivalence relationship to be upheld. **We will use ≅ to define isomorphic to** The Attempt at a Solution Let G, H, and K be groups...

Homework Statement I posted this in anther forum but I think it might be better to post it here. I was wondering if anyone could help me understand the conversion between lux and W/m2 with relation to luminous efficacy (lm/W). Thanks :) Homework EquationsThe Attempt at a Solution

<< Moderator note: Split from https://www.physicsforums.com/threads/why-do-we-need-quantum-mechanics-so-much.859210/ >> What about particle physics? It bases on QFT therefore on QM.Is that right?

Homework Statement R(ABCDEF) D->F AB->C E->F C->BD D->E Decompose R into dependency preserving 3NF Homework Equations F = {D->F, AB->C, E->F, C->BD, D->E} The Attempt at a Solution My attempt is to first construct the minimal basis for the FD set F, which is G={A->C, E->F, C->B, C->D, D->E}...

Homework Statement Homework Equations a/b=c/d The Attempt at a Solution I started out with transitivity and I figure it's transitive because a/b=e/f = af=be=(a,b)R(e,f). It can't be symmetric because ad does not equal bc, 1*4 does not equal 2*3 I'm I correct or completely wrong?

Why are ##<j_1j_2m_1m_2|jm>## and ##<j_2j_1m_2m_1|jm>## negative of each other when ##j_1+j_2-j## is odd as given below? I would expect ##<j_1j_2m_1m_2|jm>## and ##<j_2j_1m_2m_1|jm>## to always have the same sign since nature doesn't care which particle we label as particle 1 and which as...

So, after time-independent 1D Schrodinger equation is solved, this is obtained E = n2π2ħ2/(2mL2) This means that the mass of the 'particle' is inversely related to the energy eigenvalue. Does this mean that the actual energy of the particle is inversely related to its mass? Isn't this counter...

If we have Poisson bracket for two dynamical variables u and v, we can write as it is known ... This is for classical mechanics. If we write commutation relation, for instance, for location and momentum, we obtain Heisenberg uncertainty relation. But, what is a pedagogical transfer from...

I am not a mathematician but, as such, I think I have a pretty good background in mathematics. I have a good understanding and experience with calculus, differential equations, linear algebra, and probability theory. I also have interest in abstract algebra concepts, though I wouldn't say I am...

Whats the relation between compression and strength? When we build a structure, the ground or the land underneath the structure gets compressed and becomes rock solid. So how does compression make a substance strong? Is a compressed substance having more tensile strength?

Whats the relation between the centre of gravity of a structure and the middle third rule?

Homework Statement I have the following matrix: 0 0 0 1 1 0 0 0 = A 0 1 0 0 0 0 1 0 and the vector v = (1,0,0,0) If I perform Av, this gives: Av=(0,1,0,0) And If I keep multiplying the result by A like A*A*(Av), the outcome will be something like j= (0,0,1,0) k=(0,0,0,1) l=(1,0,0,0) The...

Homework Statement The problem is in the context of convection in the troposphere Show that when an ideal gas expands adiabatically, the temperature and pressure are related by the differential equation \frac{dT}{dP} = \frac{2}{f+2} \frac{T}{P} Homework Equations Ideal gas law PV = nRT...

look to post 3. original question had a lot of misconceptions.

Hello. I'm not sure if this is an A level thread however I'll just post it here. I have a question that regards dark energy in relation to space time. I've learned that dark energy only affects space and not time. However I've also learned that space and time are intrinsically intertwined as...