Modes Definition and 281 Threads

If we have the normal KG scalar field expansion: $$ \hat{\phi}(x^{\mu}) = \int \frac{d^{3}p}{(2\pi)^{3}\omega(\mathbf{p})} \big( \hat{a}(p)e^{-ip_{\mu}x^{\mu}}+\hat{a}^{\dagger}(p)e^{ip_{\mu}x^{\mu}} \big) $$ With ## \omega(\mathbf{p}) = \sqrt{|\mathbf{p}^{2}|+m^{2}}## Then why do we associate...

Homework Statement We have a rod of length L fixed to a rigid support. At the end of the rod there is a mass, m. Assume that the rod has no mass. Find the first natural frequency for the bending, axial and torsion modes. Homework EquationsThe Attempt at a Solution So I'm reviewing some stuff...

Hey, I have a question concerning eigenfrequencies: Let us assume we examine a beam that is fixed at one end and free at the other end. It is possible to get an analytical solution in form of a unlimtied series: sum_i=1..infinity eigenfunction(i)*exp(i*eigenfrequencie(i)*t). (something...

Homework Statement Homework Equations a11 = a21 = a31 = a12 = a13 a22 = a32 = a23 $$ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} =ω^2m \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}...

I am studying laser physics at the moment and there is something that confuses me. The laser output consists of the central laser mode and some axial modes due to constructive interference in the optical cavity. At first there is a high enough population inversion and while the laser works this...

Is it possible (in principle) to make a very thin phtotodetector that has the same sensitivity with respect to light coming from either side, so that we can see interference between two light waves arriving from opposite sides? That is, as we vary the relative phase shift between the right hand...

I am learning about lasers and trying to clear up some blurry concepts in my head so I am not necessary using heavy math for description here so please bear with me. Let's take EM field in a rectangular box with walls that are perfect conductors (optical cavity). EM field distribution inside...

How do dielectrics affect the number of modes for standing electromagnetic waves in a box?

Why would normal modes occur in the coupled oscillator system I.e. why the parts of system would oscillate with constant angular frequency and constant phase difference ?

So I was messing around looking at the output (423nm) of a misaligned polarization-maintaining (PM) fiber with a CCD camera, and more than once I noticed the beam profile significantly change (if you're not familiar with what PM fibers are, see last paragraph for explanation). I have video if...

Hello! I am reading some representation theory (the book is Lie Algebra in Particle Physics, by Georgi, part 1.17) and the author solves a problem of 3 bodies connected by springs forming a triangle, aiming to find the normal modes. He builds a 6 dimensional vector formed of the 3 particles and...

I am studying the modal analysis of a mechanism and I am only interested in the transverse modes, I wonder if there is a way to formulate my problem so that the results show only the transverse modes without the torsional and longitudinal ones, this would help in the post-processing a lot.

I'm trying to understand chapter 19 of these lecture notes. But I have some difficulties with what the author explains: 1) In page 176, under equation 19.3 he says: This is weird. If we are considering a local QFT, then how can he say IR physics can cause non-locality? What is he talking...

Are quantum harmonic oscillators, vacuum fluctuations and radiation modes the same? Is vacuum energy caused by vacuum quantum fluctuations?

Homework Statement Can a single mode fiber become multimode if the wavelength of the light passed through it is small enough? I put a HeNe laser (633nm) through what I thought was a single mode fiber. If it's supposed to operate at 1300nm, then would a low wavelength of 633nm cause multiple...

Hi,I have been reading a text on "Finite Element model updating". This question is not related to the subject of "Finite Element Model Updating" but rather to the subject of "Structural Dynamics" and experimental modal analysis. My questions is: 1)Let us say I have carried out a free...

Homework Statement Let's say that I have a potential ##U(x) = \beta (x^2-\alpha ^2)^2## with minima at ##x=\pm \alpha##. I need to find the normal modes and vibrational frequencies. How do I do this? Homework Equations ##U(x) = \beta (x^2-\alpha ^2)^2## ##F=-kx=-m\omega ^2 x## ##\omega =...

I'm doing an experiment measuring the relationship between length of a cantilever beam and period of oscillation when I twang it on one end, but I can't seem to understand the equation. The equation for measuring frequency is given here:https://www.hindawi.com/journals/amse/2013/329530/ but I...

Homework Statement Suppose we listen to the sound of a vibrating string with a pickup that is sensitive to the motion at a point 1/3 of the string's length from one end. Which statement is true? A.) We will be able to hear all of the modes except the third B.) We will not be able to hear the...

I understand the definition of electromagnetic LSE and LSM modes, but I'm not so sure about EH and HE modes. I realize that LSE/LSM and EH/HE are both descriptions of hybrid modes, but are they simply synonyms or something more complicated? Thanks

My question stems form the section "How Many Modes in a Cavity?" in the following derivation of Rayleigh-Jean Law: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html#c2" In here, they count the number of modes as represented by volume of an eighth of a sphere. What's the mathematical...

Homework Statement Calculate the number of modes in a cubic cavity of length a=2.5 cm in the wavelength interval (λ1,λ2) where λ1=500 nm and λ2=501 nm. What's the total energy which radiates from the cavity if it's kept at a constant temperature of T=1500 K. Homework Equations I imagine these...

Homework Statement In the book "Quantum Optics" written by Scully and Zubairy, there is an equation (1.1.5). The equation is presented directly and not explained how to be deduced. The content is as follows. Homework Equations The Attempt at a Solution I know the solution should have the form...

Homework Statement We covered the following addressing modes in class: • Absolute • Register indirect • Based (base + displacement) • Scale indexed (base + index × constant) • Memory indirect • Auto increment/decrement (by 1 byte) Consider the following high-level programs: (1) int a = 0...

I'm just looking for any tips one might have for finding normal modes quickly? The GRE always seems to have a question or two on them and I have no idea how they expect someone to do a problem like that in the time given. I know that there is normally, in the problems given, a symmetric and an...

So, my question is what does the "normal" part mean when one talks about normal frequencies and normal modes in coupled oscillations. Does it have to do with the normal coordinates that one uses when solving some problems, or with normal in the sense of orthogonal. Thanks for your help.

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...

Homework Statement Silicon crystalises in a cubic structure whose lattice is face-centred, with a basis [000],[1/4,1/4,1/4]. How many optic/acoustic modes are to be found in the phonon dispersion diagram for silicon. How many distinct branches would you expect along the [100] direction...

Homework Statement [/B] My question is more about the math of the problem. For equation 22.97, how do I construct a 3x3 matrix from a 12 element series? After constructing the matrix should I set the determinant equal to 0 where I will find the determinant has 3 solutions (2 being...

Homework Statement I have to determine the frequencies of the normal modes of oscillation for the system I've uploaded.Homework Equations [/B] I determined the following differential equations for the coupled system: \ddot{x_A}+2(\omega_0^2+\tilde{\omega_0}^2)x_A-\omega_0^2x_B = 0...

If I have a system where the following is found to describe the motion of three particles: The normal modes of the system are given by the following eigenvectors: $$(1,0,-1), (1,1,1), (1,-2,1)$$ How can I find the corresponding eigenfrequencies? It should be simple... What am I missing?

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...

A typical mode in a dielectric slab like this, with propagation along x, uniformity along z and refractive index variation along y, is represented by the following function: f (y) = \begin{cases} \displaystyle \frac{\cos (k_1 y)}{\cos (k_1 d)} && |y| \leq d \\ e^{-j k_2 (y - d)} && |y| \geq d...

Homework Statement Here's the problem. I was able to find the a_n and b_n values, my question is mainly on part (c), how do I find which modes are missing? The function is odd, so even modes should disappear, but cos(n*pi) doesn't disappear, it's either +1 or -1. I'd greatly appreciate any...

Not a textbook/homework problem so I'm not using the format (hopefully that's ok). Can someone offer an explanation of normal modes and how to calculate the degrees of freedom in a system of coupled oscillators? From what I've seen the degrees of freedom seems to be equal to the number of...

Homework Statement So, a string with length L and a mass of M is given tension T. Find the frequencies of the smallest three modes of transverse motion. Then compare with a massless string with the same tension and length, but there are 3 masses of M/3 equally spaced. So this is problem #1...

Homework Statement Good morning. I am currently doing an solid state problem; in this part, I have to tell if these vibration modes are odd or even. I am working at the lattice centre. The modes are these http://postimg.org/image/8nmv7ickz/. Homework Equations None The Attempt at a Solution...

Good afternoon. I am doing an study on ice X, a material with this structure http://postimg.org/image/nub4if9kb/ I want to know why in the centre of the brioullin zone the hidrogen atoms must remain at rest on an even mode. My reference book is Charles Kittle's, but there is no discussion about...

What determines which TEM mode will the laser output have? Why some lasers emit in TEM00, while other in a donut mode, and other in a superposition of multiple modes. Thank you.

Hi everyone, I am reading a paper, which discusses about power spectrum. There is a plot which is power versus k(wave number). It says something about "coherent large scale modes". Would you please tell me what the meaning of this is?

Homework Statement The space between 2 perfect conductor plates parallel to the x-z plane separated by a distance 2a are filled with 2 dielectric materials whose surface also lies in the x-z plane, at a distance equal to a from the plates. We're looking for TM modes propagating along the z...

Hi! How exactly is the relationship between number of atoms in the basis of a bravais lattice, and the number of possible phonon modes? So, for example, if you have 2 atoms in a basis you get 3 acoustical and 3 optical modes in 3 Dimensions. But why exactly is this? Do you need to set up the...

Hi everybody, I have been reading about gravitational waves, but I don't get how the E modes work; in one place I read that they were created during the inflation time, but in other I read that they come from the recombination. Does it mean that they were produced almost when the Big Bang...

Hi, I´ve tried to calculate the vibration modes of beam in the space, without gravity or any other force. The forumle of the beam is this one: Cos(λL)*Cosh(λL)=1 from which I´ve calculate the roots and the resonance. I´ve found a programme for Matlab that calculates the vibrations modes if...

So I've got the equation for 'allowed angles of propagation': SinΘp = pλ / 2πdnf With p is the mode, λ the wavelength, d the width and n the refractive index. I'm just not sure what to do with this equation, and my lecture notes don't go into any more detail. For example, if I knew the the max...

I've taken several courses on Electromagnetics and Waveguide. It has become common sense to me that small waveguides support less modes than larger ones. I've also learned the graphical method to calculate the number of modes in a 3-layer slab waveguide. What I don't get is why small...

Is it generally true that if you have a system of particles with some arbitrary interactions due to their relative positions which you can solve in some way (maybe numerically, maybe analytically), you can relate the long term behaviour to the undriven case if it is being driven by a...

Homework Statement The system is conformed by two blocks with masses m (on the left) and M (on the right), and two springs on the left/right has the spring constant of k. The middle spring has a spring constant of 4k. Friction and air resistance can be ignored. All springs are massless. Find...

Homework Statement (a) Explain spin and parity of mesons (b) State their quark content (c) Draw a feynman diagram of J/psi decay (d) Why doesn't ##\chi## undergo leptonic decay? (e) What is the minimum centre of mass? [/B] Homework EquationsThe Attempt at a Solution Part(a)[/B] Spin is...

Homework Statement [/B] (a) Explain lepton universality. (b) Explain why decay mode is forbidden and find hadronic branching ratios. (c) Find the lifetime of tau lepton. (d) What tau decay mode would be suitable? (e) Find the precision. (f) How do you improve the results? (g) Why is it much...