Periodic Definition and 411 Threads

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Basically, the F block is a series in the periodic table that consist of elements that are artificially synthesized. My question is, why were these elements synthesized? What was the need of synthesizing such elements?

I am trying to understand diffraction on periodic structured in solid state physics.Q is the source of the spherical wave. R the vector to the object and R+r the vector to the scattering centre P, which gives us a another spherical wave. All spherical waves are considered as plane waves due to...

Homework Statement How can I calculate the initial phase in a simple harmonic motion if I only have the amplitude, frequency and angular velocity as data? Homework Equations The formula of the position, in fact they ask me to do the formula that allows to know the elongation depending on the...

In ab initio calculations for periodic systems, only an irreducible K grid is used for calculation, and consequently only those K points have their wavefunction calculated. My question is, how to recover wavefunction at other K points not included in the irreducible K grid? Similar questions to...

https://en.wikipedia.org/wiki/Discrete_Fourier_transform Why is the signal obtained from a DFT periodic? The time signal x[n] is finite and the number of sinusoids being correlated with it is finite, yet its said the frequency spectrum obtained after the DFT is periodic. I've also read the...

I know that some functions are ## 2 \pi ## periodic but what does it mean that a function is ##1##-periodic. Is it ##f(x+1n) = f(x)## where ## n \in \mathbb{Z} ## ?

Hello people, I have 3 questions related to the mean speed of electrons in a period potential /lattice. I've read Ashcroft and Mermin's page 139 as well as the Apendix E. From what I understood, if one applies the momentum operator on the wavefunction of a Bloch electron, one doesn't get a...

Hello everyone! I'm trying to get a deeper understanding on how to determine those periodic orbits in the equal-mass three-body Newtonian gravitational problems. The most general idea I know is to confine the three bodies into a zero angular momentum space, which sounds vague to me. What is the...

Loosely speaking, we say that periodic orbits are 'dense' if given any $\epsilon$-neighborhood, there exists at least one periodic point in that neighborhood for any $\epsilon > 0$. Is there any requirement for these periodic points to be unique? For example, what if every neighborhood...

Hey, I need to prove that dirichlet function is a periodic function, but i got no idea how to start solving the question. could anyone help please?

Hi, Is this possible to represent a periodic function like a triangular wave or square wave using a Taylor series? A triangular wave could be represented as f(x)=|x|=x 0<x<π or f(x)=|x|=-x -π<x<0. I don't see any way of doing although I know that trigonometric series could be used instead...

Homework Statement A particle moving in a periodic potential has one-dimensional dynamics according to a Hamiltonian ## \hat H = \hat p_x^2/2m+V_0(1-cos(\hat x))## a) Express ## \frac{d <\hat x>}{dt}## in terms of ##<\hat p_x>##. b) Express ## \frac{d <\hat p_x>}{dt}## in terms of ##<sin(\hat...

Homework Statement Find Fourier coefficients of the periodic function whose template is x(t) where the Fourier Transform of x(t) is X(f) = (1-f^2)^2 where \left|f\right|<1 and period T_0= 4. Homework Equations FC=\hat x_T(k,T_0)=\sum_{k=-\infty}^\infty\frac{1}{T_0}X\left(k/T_0\right) The...

Hello, I am attempting to solve the 1 d heat equation using separation of variables. 1d heat equation: ##\frac{\partial T}{\partial t} = \alpha \frac{\partial^2 T}{\partial x^2}## I used the standard separation of variables to get a solution. Without including boundary conditions right now...

Homework Statement I have the heat equation $$u_t=u_{xx}$$ $$u(0,t)=0$$ $$u(1,t) = \cos(\omega t)$$ $$u(x,0)=f(x)$$ Find the stable state solution. The Attempt at a Solution I used a transformation to complex to solve this problem, and then I can just take the real part to the complex...

!HELP! The Singapore Flyer, until recently the world's largest Ferris wheel, completes one rotation every 32 minutes.1 Measuring 150 m in diameter, the Flyer is set atop a terminal building, with a total height of 165 m from the ground to the top of the wheel. When viewed from Marina Centre, it...

If you know the velocity of an object as a function of position Can you use a uniform distribution over one period and the object velocity to perform a change of variables for the positional probability. Example. X(t)=Asin(wt) V(t)=Awcos(wt) V(X)=+-Aw(1-(X/A)^2)^(1/2) P(t)=1/T T=Period Change...

Hi. I'm a student of electrical engineering, and I've always been interested in the idea of electrical cars, so I came up with a question: let's suppose we want to have a normal trip with car, and then we're not interested in going so fast with it. When we are driving in this condition, it isn't...

Hey, I hope you can help me. I can't understand why periodic function is Time Variant. thanks Dor.

Homework Statement Three periodic currents have the same ##f=100 Hz##. The amplitude of the second current is ##4 A##. and is equal to half of the amplitude of the third current. Effective value of the third current is 5 times that of the first current. At time ##t_1=2ms## third current...

So far, I have taken General Chemistry I and II, and Organic Chemistry I. Out of these classes, only General Chemistry I seems to make use of the periodic table, but it is mostly just going through the basics of the periodc table. Not so much in Gen Chem II or Orgo I. I mean they give it to you...

Homework Statement "Each piston of an engine makes a sharp sound every other revolution of the engine. (a) How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? (b) At how many revolutions per...

Is there a period trend for bond enthalpy? Specifically Atom-Hydrogen bonds. Need to find a trend in predicting the bond enthalpy of several atom-hydrogen bonds I calculated using gaussian. Any help would be appreciated, thanks!

Hi, I need to teach a lesson on electrons in periodic potentials for Bachelor Physics students in just 20 minutes Any ideas on how to organize the lesson (pre-concepts they should know, relevant message and consequences) would be very much appreciated

(Mentor note: moved here from noon homework thread hence no template) I was studying vibration of a one-dimensional monatomic chain and the textbook used periodic boundary condition (PBC). I wanted to justify the use of PBC, so I came up with this: atoms deep inside the crystal sees an...

Homework Statement Homework Equations I'm not sure. The Attempt at a Solution I started on (i) -- this is where I've gotten so far. I am asked to compute the Fourier transform of a periodic potential, ##V(x)=\beta \cos(\frac{2\pi x}{a})## such that...

Hi, I'm trying to understand the bound states of a periodic potential well in one dimension, as the title suggests. Suppose I have the following potential, V(x) = -A*(cos(w*x)-1). I'm trying to figure out what sort of bound energy eigenstates you'd expect for a potential like this. Specifically...

Homework Statement ##\Omega = {nw_1+mw_2| m,n \in Z} ## ##z_1 ~ z_2 ## is defined by if ##z_1-z_2 \in \Omega ## My notes say ##z + \Omega## are the cosets/ equivalence classes , denoted by ##[z] = {z+mw_1+nw_2} ## Homework Equations above The Attempt at a Solution So equivalance classe...

Homework Statement Consider the set V + {all periodic *complex* functions of time t with period 1} Draw two example functions that belong to V. Show that if f(t) and g(t) are members of V then so is f(t) + g(t)Homework EquationsThe Attempt at a Solution f(t) = e(i*w0*t)) g(t) =e(i*w0*t...

Can combination elements in group I and group VII be a semiconductor? My thinking is that they form the octet rule just like group II and group VI elements.

Homework Statement Let f : R → Rn be a smooth function. Give necessary and sufficient conditions on f so that the antiderivative F(x) = ∫f(t)dt (from 0 to x) is periodic with period p ≠ 0 Homework EquationsThe Attempt at a Solution My initial thought is that as long as f is periodic then F...

Homework Statement Explain why the first four rows of periodic table have 2, 8, 8 and 18 atoms respectively Homework Equations I have a feeling this has something to do with the central field approximation OR the s, p, d, f orbitals and how many electrons can go in each OR something else The...

Heres an example. Let G(s) be the moving average of all previous values of f(s). G(s) and F(s) intersect at multiple points. Is it possible to prove that the intersections happen periodically?

< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown >[/color] Hi all. I'm completely new to these forums so sorry if I'm doing anything wrong. Anyway, I have this question... Find the Fourier series for the periodic function f(x) = x^2 (-pi < x < pi)...

Hello everybody, I have some questions about treatment of Schrodinger equation where ## \hat{V}(\theta)##, the potential energy part of Hamiltonian ##\hat{H}=\hat{T}(\theta)+\hat{V}(\theta)## is a trigonometric function like: ##\hat{V}(\theta) = a sin(\theta)## or ##\hat{V}(\theta) = a...

Hi all, I am reading something on wave function in quantum mechanics. I am thinking a situation if we have particles distributed over a periodic potential such that the wave function is periodic as well. For example, it could be a superposition of a series of equal-amplitude plane waves with...

They certainly do sound periodic from observation. But is there a particular formula that proves that sound from Newton's Cradle is periodic?

A tad embarrassed to ask, but I've been going in circles for a while! Maybe i'll rubber duck myself out of it. If $$f(t) = f(t+T)$$ then we can find the Fourier transform of $$f(t)$$ through a sequence of delta functions located at the harmonics of the fundamental frequency modulated by the...

Consider the following mechanical system A thin tube can rotate freely in the vertical plane about a fixed horizontal axis passing through its centre ##O##. A moment of inertia of the tube about this axis is equal to ##J##. The mass of the tube is distributed symmetrically such that tube's...

Say we have a periodic sequencs, ABCDABCDABCDA... etc. We would normally call A term 1, B term 2, C term 3, etc. However, to find the nth term, do we need to designate A as term 0, B as term 1, etc? Since we would use n mod 4 to find the nth term, wouldn't this mean that 4, 8, 12, etc would have...

Homework Statement Homework Equations none The Attempt at a Solution a) It is a periodic relationship because the number of hours of daylight repeats each year? OR It is a periodic relationship because the number of hours of daylight is based on the rotation of the earth, which is also...

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...

g(t)=½( f(t)+f(-t) ) h(t)=½( f(t)-f(-t) ) show its 2π periodic so: g(t+2π) = ½( f(t+2π)+f(t-2π) ) why does -t become t-2π ? ½( f(t)+f(-t) ) = g(t) h(t+2π)=½( f(t+2π)-f(t-2π) ) ½( f(t)-f(-t) ) = h(t) is this correct? can...

Homework Statement Homework Equations no equations required The Attempt at a Solution [/B] a) The number of hours of daylight is a periodic relationship, because it repeats the same wave-like pattern over the course of 1-2 years. b) the period is the amount of time it takes for one cycle...

Homework Statement What is the fundamental period of the expression sinx/sinx.can you guys please illustrate how to make its graph? Homework Equations Okay I know drawing graph can give me the period.Can the period be found by any other method? The Attempt at a Solution I'm told that the...

Homework Statement So i have a function f(x)=x^2 that is periodic -a<x<a and need to sketch this function from -3a<x<a. I know how to find the Fourier coefficients though. Homework Equations f(x)=x^2 sketch it periodically The Attempt at a Solution I know that a function is only periodic...

Homework Statement Find maximum and minimum values for the depth of h of the water If a periodic function has f(2) = 1 and f(5) = 0 predict what f(8) , f(-10), and f(11) will be.[/B] Homework EquationsThe Attempt at a Solution f(8) = (6+2) = f(2) = 1 f(-10) = (-6-6+2) =f(2) =1 f(11) = (6+5)...

My experience with data fitting is poor so I am in real need for help. The potential in the following is periodic over [0,Pi] I need to find a fitting function that I can use to perform further mathematics. Fourier series does not work, but a 40-degree polynomial give the following fit...