Relation Definition and 1000 Threads

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...

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 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?

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...

Homework Statement This isn't actually a homework question.Actually, it's an example from Rosen's Discrete Math and Its Applications that I'm having difficulty with: "A computer system considers a string of decimal digits a valid codeword if it contains an even number of 0 digits. For...

We all know the famous mass-energy relation E=mC^2,but my question is what does this really mean.I mean if I apply this equation for a normal practical application case e.g. burning of wood,the energy I will get from this combustion reaction will be equal to the mass I used multiplied by C^2.Is...

Someone texted me and asked me if the Earth was half as massive what impact would that have on the rotation period of the moon? I'd think that the moon would rotate slower as it's gravity would more influence on the earth. But I am not sure if that makes sense or not haha

If I were to drop a ball down a fluid with high viscosity, the ball decelerates over time and then reaches close to terminal velocity. How does displacement and velocity relates with time in terms of mathematical equation? Am I right to say: v(t) = Vterminal(1 - exp(-bt)) d(t) = Vterminal*t(1 -...

I'm doing a small research project on group theory and its applications. The topic I wanted to investigate was Noether's theorem. I've only seen the easy proofs regarding translational symmetry, time symmetry and rotational symmetry (I'll post a link to illustrate what I mean by "the easy...

Hi, Assume a matrix H n\times m, with random complex Gaussian coefficients with zero-mean and unit-variance. The covariance of this matrix (i.e., expectation [HHH]) assuming that m = 1 is lower than another H matrix when m > 1 ?? If this holds, can anyone provide a related reference? Thanks...

In quantum mechanics, a physical quantity is expressed as an operator G, then the unitary transformation coresponding to the physical quantity is expressed as exp(-iG/ħt), being also an operator, where t is the tranformation parameter. G is actually the conservative quantity corresponding to the...

Homework Statement In a certain region of space, the electric field along the x-axis is given by: E = 1.2x - 3.06, where E is in N/C and x is in meters. If you set the electric potential equal to zero at (4.39 m,0), find the electric potential, in V, at the point (7.22 m,0). Homework...

I am reading this: http://arxiv.org/pdf/quant-ph/0609163.pdf And Demystifier claims that "The time-energy uncertainty relation is not fundamental" However the proof is done in non-relativistic QM, where t and x are treated differently. My question is, what's about relativistic QM?

Homework Statement Let ##G## be a group and ##\sim## and equivalence relation on ##G##. Prove that if ##\sim## respects multiplication, then ##\sim## is the equivalence relation associated to some normal subgroup ##N\trianglelefteq G##; i.e., prove there is a normal subgroup ##N## such that...

hi, i have studied the annihilation and creation operators and number operator N in relation with the simple harmonic oscillator that is governed by: H = hw(N+1/2) i don't understand the relation between the harmonic oscillator and for example, this hamiltonian: H = hw1a+a+hw2a+a+aa that i...

Hey! :o We have the following lemma: Assume that the characteristic of $F$ is $p$ and $p>2$. Then $(t^m-1)/(t^n-1)$ is a square in $F[t, t^{-1}]$ ($F[t,t^{-1}]$: the polynomials in $t$ and $t^{-1}$ with coefficients in the field $F$) if and only if $(\exists s \in \mathbb{Z}) m=np^s$. Can...

Electrons are accelerated in an electrical potential of: ΔΦ = 105 V and are focused on a biological specimen. Assume that the kinetic energy of an electron is given by eΔΦ where e is the charge of an electron. What is the smallest possible object that can be resolved assuming that the...

I almost feel embarrassed to ask this. I've always understood it to be that the higher the frequency, the higher the energy (at least from what I've been taught). However, something has always bugged me: why then, when a medium is involved, are the lower frequencies the ones that make it...

Homework Statement Which solid-line curve most accurately represents the distribution of molecular energies in a gas at 500 K if the dotted-line curve represents the corresponding distribution for the same gas at 300 K? Homework Equations - The Attempt at a Solution Not sure how this...

Hi, just curious. Sorry I am trying to get a handle on this , will try to make it more precise: I am trying to see if the following has a categorical parallel/counterpart. Consider the case of measure spaces (X,S,m) : X any space, S a sigma algebra, m a measure and that of metric spaces (Y,d)...

[don't know whether i is the correct thread prefix, will change if requested/possible] Now I will start off by saying I'm only an interested lay person, and haven't studied this but was thinking about time dilation and it's correlative effects with gravity. Higher gravity, time slows down...

Hello all, Is there any direct relation ship exists between the thermal expansion and density of polymer material (eg. PMMA, Teflon) ? Like, Lorentz- lorentz law relates directly the refractive index and density of the polymer. similarly any laws relating (thermal expansion and density of...

I'm very sure this is wrong. I think the f^i(x) should be changed to a g^i(x) where g^i(x) is some function (I'm guessing either Gamma or Beta) and that the infinity sign should be changed to a i-->k where k is some arbitrary value. Reason being f^i(x) will always equal zero and j/i! will also...

My textbook says "The lower the gas pressure, the higher the mean-free-path". But it does not explain why. Can someone please explain it briefly? Thank you very much.

Good day (or night). I am new here, so I hope my question doesn't bother many. If (forgetting other laws of nature) a shoebox where to hit the sound barrier and an F-35 were to do the same. Would the sound waves be equal. Would it sound the same to a ground observer? I always assume that mass...

Hi first post so forgive any break in widely accepted conduct, Currently involved in a physics competition one of the question is to investigate geysers. Time and time again I have stumbled upon reference to Clausius-Clapeyron relation. Probably the best source I have come across is a youtube...

I have come across this inequality:$$ g≤ log\ n <g + 1$$ We assume that the base of the log is b >1 and n is all the natural numbers. I would like to know if anyone could provide a proof regarding this and mention for what g ? Is it for all the g which are integers ?

Where is the fifth energy level in relation to the fourth energy level? Well, it shows that energy level five is at n= 5 and energy level four is at n=4 away from the nucleus, so that means that the fifth energy level is at the 16th orbital and energy level four is at the 25th orbital?? I am not...