Relation Definition and 1000 Threads

Below I have uploaded the page I am having trouble with. Here it says that it is using induction on n but I don't understand how it uses the formula for when n=j to derive the formula for when n=j+1

Hello! (Wave) TheoremIf the vector field $\Phi(x,t)$ satisfies the Lipschitz condition as for $x$ and is continuous as for $t$ in a space $\Omega \times (a,b) \subset \mathbb{R}^{n+1}$, then there is at most one solution of the system $\frac{dx}{dt}=\Phi(x,t) (1)$, that satisfies the initial...

Is there a formalism that relates the properties of energy (electromagnetism) to the properties of spacetime (relativity)?

I am having a lot of difficulty understanding this concept. Suppose you have two objects A,B of mass A',B' connected by a massless rope. Let K Newtons be the force applied on object A .What is now the tension along the rope ? -My reasoning: K Newtons is the force applied to the combination...

Dear Community, I get the following relation with the help of Wolfram Mathematica: $$ U\left[a,1,z\right] = \frac{1}{\Gamma\left[a\right]^2\Gamma\left[1-a\right]} \int_{0}^{1} U\left[1,1,zk\right]k^{a-1}(1-k)^{-a}dk $$ I would like to justify this identity in order to use in my article. I do...

If the gene is smaller, is the protein that it codes for smaller too? Vice versa?

Hello, What is the energy dispersion relation and density of states for graphen near the Dirac point ? I am looking for a proper graph illustrating these properties.

In the weak field limit, we have dt = (1 + 2\phi)^{-\frac{1}{2}}d\tau where the usual meaning of the symbols applies. This means that in GR dτ < dt analogous to SR. Let suppose we measure the period dtS of a photon emitted at the surface of the Sun as well as the same photon, i.e. same atomic...

I know that 1. To show the relation is reflexive, we need to show that for any x, using the definition of R, we have xRx. The definition of R means that we must have |x - x| is even.2. To show that R is symmetric, we would have to show that if xRy then yRx. In the context of the definition...

I state that I am a beginner in QFT, but it seems to me that the methods to regularize the integrals of the perturbation series before renormalize serve to cut off the high-energy modes that are responsable for the UV divergences. This ( the cut off of high-energy modes ) nevertheless is not so...

For an electron can I not do the following to determine both the position and momentum? I take a screen with a small hole and I eventually make the hole smaller and smaller. Cathode rays emitted will hence get diffracted after passing through the hole making momentum more and more uncertain...

Let us define a relation a on the set of nonnegative real triples as follows: (a1, a2, a3) α (b1, b2, b3) if two out of the three following inequalities a1 > b1, a2 > b2, a3 > b3 are satisfied. a) (3) Test a for Transitivity and Antisymmetry We call a triple (x, y, z) special if x, y, z...

I would like to perform some modelling on spiral galaxies learning about the Baryonic Tully-Fisher Relationship. Does anyone know of a catalog where I can find the maximum velocity (Vflat ) and radius (of Vflat ) of galaxies? (Yes, I know the Tully-Fisher relationship only relates tangential...

Hi, Two questions. 1) I'm having trouble understanding the stability of the stable Lagrangian points (L_4 and L_5); Wikipedia explains that if an object in the L_4 or L_5 of a planet is pushed closer towards the common center of gravity of the Sun and the planet, the increased speed that comes...

I'm trying to figure our the relation between cross section, scattering angle and KE? I'm doing a few exercises where I've been given kientic energy and scattering angle and have to calculate the cross section. Cross section is in units of Barns (m2), and KE is 1/2 kg*m2*s-2, but I can't seem...

For someone who's familiar with the de Broglie relation it's easy to say that for k=0 we have p=0 but how would we know that before deriving the result? In this image the author derives de Broglie relation by considering a wave packet in motion. As you can see where I have star-marked the author...

Homework Statement What is the Lorentz-transformation that one would use to go from the lab frame to the Breit Frame? [/B]

I have a question about what I would call a relation inside a relation. Like: A={1,2,3) and B={a,b,c} R1={(a,1) ,(a,3), (b,2), (c,1,), (c,3) } R2={(a,a), (b,a), (b,c), (c,a) } R3=R1R2 Like this. I have 2 regular relations. Then I form another relation using these 2. How do I do that? Like...

Hi All, My apologies, I think I may have asked this question already, but I could not find it. Here it goes: I have seen the usage of the word 'relation', specifically a relation between tables but I have not seen a formal definition. From what I understand, tables X,Y are related to each other...

Is there a relation between the fact that the derivative of x^2 is 2x and that the difference between 1,4,9,16, ... is 3, 5, 7, 9, ...? And why is the difference always 2?

I need to get a few things straight about the integration operation (as an intro calc student). I understand that integration is a process that takes a function and returns its antiderivative. We can think of it as an operator, where ##\displaystyle \int...dx## is kind of like an opening and a...

Hello good people, please refer to this: (notice the mistake in 9.31: cos(psi) switches places with cos(phi)sin(psi) to the best of my understanding) Now, I am trying to derive 9.30 and for this, according to the book, we solve 9.32. The problem is I can not understand 9.32, the meaning of...

Homework Statement a) Find a rec. rel. for an, the number of sequences of length n formed by u's, v's, and w's with the subsequence vv not allowed. b) Repeat part a) but now with the requirement that there is no subsequence uwv. The Attempt at a Solution a) the first letter in the sequence can...

I have the recursion relation ##y_{k}=k(2j-k+1)y_{k-1}## and I would like to solve it to obtain ##y_{k}=\frac{k!(2j)!}{(2j-k)!}##. Can you provide some hints on how I might proceed? P.S.: ##j## is a constant.

I'm trying to relate different ways of getting a value for the "width" of a non-parallelogram. The non-parallelogram is given in figure 1: note that the left-hand side edge is vertical, the right-hand side is tilted 4 degrees away from vertical, and the bottom edge is 24 degrees below the...

Hey Friends, In Einstein's special relativity I find "Twin Paradox", where Dick and Jack, two twins . one of them went to space at a speed of 0.80c to a star 20 light year away (where c is the speed of light) and other remains on earth. When Jane returned to Earth his age was...

Hello, Assume that H is a n \times m matrix with i.i.d. complex Gaussian entries each with zero mean and variance \sigma. Also, let n>=m. I ' m interested in finding the relation between the distribution of HHH and HHH, where H stands for the Hermittian transposition. I anticipate that both...

I was going through Periodic Motion chapter of my book and came across an equation while defining the relation between Time Period of on oscillating particle and force constant. k/m=w2 which was applied in, T = 2xpie/angular velocity can anyone please help me define this equation. I can't seem...

Consider this self-evident proposition: "If object A has the same mass as object B and object C separately, then object B has the same mass as object C." Why isn't this stated as a law, but the zeroth law of thermodynamics is? Is there a physical quantity u such that the u of A is equal to the...

I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level). 1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...

I now study general relativity and have a few questions regarding the mathematical formulation: 1) What ist the relation between an connection and a covariant derivative? Can you explain the exact difference? 2) One a lorentzian manifold, what ist the relation between the...

Hi, Consider the conservation laws for an isothermal linear incompressible flow governed by the mass and momentum equation. The kinetic energy equation is then solved to see if energy conserved. Can anyone tell me if once it is shown energy is conserved, it implies that convergence is obtained...

Is there an accepted term for the symmetric counterpart of a matrix element? Tried searching the web but didn't really seem to find such a term mentioned anywhere.

Homework Statement [/B] If electron (1) is in a state described by cosα1χ+ + sinα1e iβ1 χ- and electron (2) is in a state described by cosα2χ+ + sinα2e iβ2 χ-, what is the probability that the two-electron state is in a triplet state? The Attempt at a Solution I already solved this problem; I...

Book states: $\nabla f\left(u, v\right) =0 = \frac{\partial f}{\partial u}\nabla u + \frac{\partial f}{\partial v} \nabla v, \therefore \nabla u$ and $ \nabla v $ are parallel 1. I know $d f\left(u, v\right) = \frac{\partial f}{\partial u}du + \frac{\partial f}{\partial v} dv$, but how can...

Homework Statement This is just a problem to help me understand. Determine the dispersion relations for the three lowest electron bands for a 1-D potential of the form ##U(x) = 2A\cos(\frac{2\pi}{a} x)## Homework Equations I will notate ##G, \,G'## as reciprocal lattice vectors. $$\psi_{nk}(x)...

Homework Statement Show that the uncertainty relation can be written as Δλ Δx >= λ^2 /4π Homework EquationsThe Attempt at a Solution Ok the uncertainty relation is ΔpΔx >= h/2π , also p = h/λ , so substituting that I have Δh/λ Δx >= h/2π , then divide both sides by h, and multiply both sides...

Homework Statement 1. Show that the Lorentz algebra generator ##J^{\mu \nu} = i(x^{\mu}\partial^{\nu}-x^{\nu}\partial^{\mu})## lead to the commutation relation ##[J^{\mu \nu}, J^{\rho \sigma}] = i(g^{\nu \rho}J^{\mu \sigma} - g^{\mu \rho}J^{\nu \sigma}-g^{\nu \sigma}J^{\mu \rho}+g^{\mu...

I am stuck on this Self-test 1.6 in molecular quantum mechanics by atkins and friedman. Probably making use of the completeness relation the question is the following: Show that if <Ωf>*=-Ωf*, then <Ω>=0 for any real function f. Anyone got a clue?

I am stuck on this Self-test 1.6 in molecular quantum mechanics by atkins and friedman. Probably making use of the completeness relation the question is the following: Show that if <Ωf>*=-Ωf*, then <Ω>=0 for any real function f. Anyone got a clue?

Homework Statement Use the formulas given (which have been solved in previous questions) prove that where w_12 is a complex constant. From here, induce that where eps_abc is the fully anti-symmetric symbol Homework Equations The equations given to use are: The Attempt at a...

OK, I have never had physics till this semester and I am in calculus based physics and it is kicking my butt. I don't understand how derivatives are properly used in the formulas, and I have an example, my question is the image attached. @=theta A=alpha SO, A) I need omega (angular velocity)...

Homework Statement The (classical) energy of one-dimensional linear oscillator is a) show, using the uncertainty relation, that the energy can be written as b) Show that the minimum energy of the oscillator is Where Homework Equations Δp Δx >= ħ/2 p ≈ ħ/2x The Attempt at a Solution I'm...

In an earlier thread of mine, another physics forums member was nice enough to point out that there is an uncertainty relation between photon number and wave phase for light. https://www.physicsforums.com/threads/is-there-a-frequency-eigenstate-for-light.727141/ Now I am wondering, where does...

Hey! :o How can we solve the following recurrence relation? $$f_n=\left (\frac{2}{a^2}+b\right )f_{n-1}-\frac{1}{a^4}f_{n-2} \\ f_0=1, f_{-1}=0$$ I calculated some values to see if there is a general pattern, but it doesn't seems so... $$f_1=\left (\frac{2}{a^2}+b\right ) \\ f_2 =\left...

Hello! (Wave) What does a loglog-graph represent? For example if we have the following loglog-graph, which is the relation between $N$ and $E$ ?

I have dug several resources from the internet, but none happen to explain the following formula: ##1 = \int \frac{dp}{(2\pi)^{3}} |\vec{p}><\vec{p}|## I have done basic quantum mechanics, so I know that this is the completeness relation. Also, I understand that an integral is being taken over...

The O(N) nonlinear sigma model has topological solitons only when N=3 in the planar geometry. There exists a generalization of the O(3) sigma model so that the new model possesses topological solitons for arbitrary N in the planar geometry. It is the CP^{N-1} sigma model,†whose group manifold is...

Hey, I am trying to understand electron transport in 2D semiconductors. One question keeps lingering in my mind is whether the Einstein relation holds for these 2D materials. The only literature I can find is back to 1997 (http://arxiv.org/ftp/arxiv/papers/1004/1004.1717.pdf). The author...

Homework Statement Find the driving frequencies at which the mechanical energy of the forced oscillation is 64 % of its maximum value. (Do not assume weak damping.) Homework Equations E∝A2ω2, where A is amplitude & ω is the angular frequency. The Attempt at a Solution Of course this...