Square Definition and 1000 Threads

Homework Statement The value of √i + √-i , where i=√-1 is (a) 0 (b) 1/√2 (c) √2 (d) -√2 Only one option can be chosen Homework Equations The Attempt at a Solution Let (x + iy)2=i Solving for x and y, I got √i = +1/√2 (1+i) or -1/√2...

Homework Statement Find a power series for f(x) = \frac{1}{\sqrt{4+x^{2}}}, at x=0. 2. The attempt at a solution I have looked up the Taylor series of \frac{1}{\sqrt{4+x^{2}}}, but I don't find any similarity with a power serie like \sum_{n\geq 0} a_{n} x^{n} I don't know how to start...

help I am stumped on this ((x2)/18)-(x/9)=1(Headbang)(Headbang)(Headbang)(Headbang)

Given a quadratic form: x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2, find the symmetric matrix that defines this, row reduce this matrix into row echelon form, and use this upper triangle matrix to complete the square and write the quadratic form as the sum/difference of...

Homework Statement Complete the square using the symmetric matrix that defines the given quadratic form: ##x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2## and write this quadratic as the sum and difference of squares after completing the square using the matrix. The Attempt at...

Homework Statement An electron in an infinitely deep square well has a wave function that is given by http://postimg.org/image/s159u7ynt/ What are the most probable positions of the electron?The Attempt at a SolutionI got the values as L/6, L/2, 5L/6 by finding the x values that made the wave...

I ordinarily would put this up in a homework/ coursework forum, but this isn't either one, its just something I was curious about given that I am in a Mechanics class. So, I have done calculations for finding the gravitational force from a sphere and from a ring, and a flat circular plate. All...

I have started coming across square roots (H+kI)^{\frac 12} of slight modifications of Schrodinger operators H on L^2(\mathbb R^d); that is, operators that look like this: H = -\Delta + V(x), where \Delta is the d-dimensional Laplacian and V corresponds to multiplication by some function. But...

how does $$\frac{5700}{\sqrt{15,300}}$$ turn into $$\frac{570}{\sqrt{153}}$$ ??

Homework Statement Suppose that the magnetic eld in some region has the form B = kzx(hat). (where k is a constant). Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current I, flowing counterclockwise, when you look down the x axis...

My question is: Researching two sizes of square steel tubing to use for a project. material 2 inch square tubing with 0.25 thick wall and 3 inch square tubing with 0.25 thick wall. The square steel tubing will be welded on to a frame at an angle so the corners point up and down , or another...

Hi, a long time ago, back in high school, I remember my teacher was explaining the force of gravity to us. He gave us the equation for the force of gravity, which was proportional to the inverse square of the distance. However, he later said that something about Einstein and other researchers...

Homework Statement Given a square and the respective distension tensor, ε, find the position on his vortices after the transformation. ε = 0.1...0.25 ...0.25...0.1 Homework Equations The Attempt at a Solution I got kind of lost in this question. I started thinking that maybe...

Homework Statement Show in the graph ,there will be no allowed bound states with odd-parity if the well depth is less than ${V_min}$ Find ${V_min}$ in terms of k and a.where a is the half of the well width. What does no allowed bound state mean? Homework Equations $cotz=-pa/z$ where p^2...

Hi, I am new here and I don't know if anyone is going to answer to this post, but if you do so thank you very much. I have been frowning on these kind of problems! I have been trying to solve some exercices from my homeworks. However, I don't know if I am doing them correctly. Here is one...

I have stumbled upon an approximation to the average of integer square roots. \sum^{n}_{k=1}{\sqrt{k}/n} \approx \sqrt{median(1,2,...,n)} Sorry I am not very good at LaTeX, but I hope this comes across okay. Could anyone explain why this might be happening? In fact, I just discovered that...

Homework Statement A small bead is on square loop in the xz plane with dimensions (±R, 0, ±R). An electric field is turned that is ##\vec{E}(\vec{r})=-Cx\hat{z}## Calculate W Homework Equations ##W= \int q\vec{E}\bullet dl## The Attempt at a Solution Starting with z direction...

Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node150.html Again we have assumed a beam of definite momentum incident from the left and no wave incident from the right. Why is the above statement made? What does the reflected wave mean? There is now all why reflected...

My understanding is that a classical idealized particle, moving in one dimension, with momentum p and kinetic energy T comes into contact with an infinite step-function potential V, there will be an (instantaneous) elastic collision - the particle's momentum becomes -p, so its energy remains...

I was looking over my notes today, and I realized that there was a point that isn't pretty clear. If we have the image under T (being T a matrix transformation induced by a matrix A) of the unit square, then its area should be abs(det(A)). Why is this though? I was looking at the proof and I...

number cannot be prime? I have checked this for n from 3 to 53,509, the latter being the limit for unsigned int. I believe this is true, and I thereby claim that this is a true statement. However, I don't see any obvious explanation for it.

Homework Statement lim x-> 2+ f(x)=sqrt(4-x^2)whats the value of the following function?? Homework Equations The Attempt at a Solution i tried and got the answer as does not exist but some people got it as 0 which is the correct answer

Hey guys, this is my first post so go easy on me. I was looking over the simple case of a 1D particle restrained inside an infinite square well potential ("particle in a box") and was having some difficulty understanding the relationship between the energy states and the expectation value for...

Homework Statement Solve for ##L^2_x## ##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry! Homework Equations Solve for ##L^2_x## ##L_x = \frac{\hbar}{i}...

Hi all, my friend is writing a sci-fi/fantasy book and for it he asked me for a function that generates a vector field like picture A. So far the closest I've got is i*-(1/x)+1/-yj, which generates B. How would I generate B without using conditions? any help appreciated, thanks.

A seemingly good way to understand the overshoot and decay (ringing) of a square wave on a scope is that it is the result of bandwidth limiting. In that case, the Fourier series of a square wave \Pi(t) = \frac{1}{2 \pi} \sum_{n=-\infty}^\infty \frac{\sin(n \omega/2)}{n \omega/2} \exp(i n \omega...

I'm looking to get some help understanding the tachometer out specifications for an MSD 6AL ignition control unit. It specifies that "The Tach Output wire produces a 12 voltage square wave signal with a 22.5° duty cycle." I'm fine with the fact that its a 12 volt square wave, but I'm a...

Hello, I was wondering if I could get some advice on how to build a robot that can traverse the inside of a twisting square tube, whilst staying at its centre. Heres an image of the kind of tube it will be: Its probably doable with a rollercoaster style design but it seems like an...

Homework Statement Particle in well: V(x)=0 for |x|<\frac{L}{2} V(x)=∞ for |x|>\frac{L}{2} initial wave function \Psi(x,0)=\frac{1}{√L}[cos\frac{\pi*x}{L}+ i*sin\frac{2*\pi*x}{L}] a) calc P(p,t) (momentum prob density) Homework Equations Anything from Griffiths QM The Attempt at a...

Good morning everyone, I am taking a signals and systems course where we are now studying the Fourier series. I understand that this is for signals that are periodic. But I get hung up when determining the Fourier coefficients. In the video by Alan Oppenheim, he derives the equation for...

Homework Statement A particle of mass ##m## is trapped between two walls in an infinite square well with potential energy V(x) = \left\{ \begin{array}{cc} +\infty & (x < -a), \\ 0 & (-a \leq x \leq a), \\ +\infty & (x > a).\end{array} \right. Suppose the wavefuntion of the particle at time...

Homework Statement A particle, mass m propagates freely in a box, length L. The energy states are: ϕ_n(x) = (2/L)^(1/2)sin(n∏x/L) and energies E_n = n^2∏^2/(2mL^2) at time t=0 the system is in state ϕ_1 and the perturbation V=kx is applied (k constant) and turned off at t=T...

Homework Statement Consider a charged particle of mass m in a harmonic potential and in the presence also of an external electric field E = E\hat{i}. The potential for this problem is simply V(x) = 1/2 mw^{2}x^{2} - qεx where q is the charge of the particle. 1) Show that a simple change of...

Homework Statement An electron in a one-dimensional infinite square well potential of length L is in a quantum superposition given by ψ = aψ1+bψ2, where ψ1 corresponds to the n = 1 state, ψ2 corresponds to the n = 2 state, and a and b are constants. (a) If a = 1/3, use the normalization...

Sorry for the wording of the topic- I couldn't figure out how to make it fit. If I passed a hypothetical square wave through a material- be it wood, glass, cotton, etc.- would it change to look more like a sine wave?

Homework Statement Im trying to prove that if p is prime, then its square root is irrational. The Attempt at a Solution Is a proof by contradiction a good way to do this? All i can think of is suppose p is prime and √p is a/b, p= (a^2)/ (b^2) Is there any property i can...

1. The problem is in the attachments 2. Basic chemistry knowledge 3. The radius of one Rb atom is 4.95/2 time 10^-8 cm, we calculate the area then divide 9 into the area of one atom, we get the number of atoms, why is 4.7 x 10^15 atoms wrong?

Can someone show me step by step guide,how to find all possible solutions for example?

Suppose you have an electron in the infinite square well. The system is completely isolated from the rest of the world and has been its entire lifetime. Do we then know that the wave function describing the electron is an eigenstate of the Hamiltonian? The question arose because I was given a...

Hi, I am trying to make progress on the following integral I = \int_0^{2\pi} \sqrt{(1+\sum_{n=1}^N \alpha_n e^{-inx})(1+\sum_{n=1}^N \alpha_n^* e^{inx})} \ dx where * denotes complex conjugate and the Fourier coefficients \alpha_n are constant complex coefficients, and unspecified...

A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...

Homework Statement Show for a simple square lattice that the kinetic energy of a free electron is higher at the corner of the first zone than at the midpoint a side face by a factor of 2. Homework Equations Simple geometry. The Attempt at a Solution I think I know how to solve, but...

Hello everyone, What is the square root of a square of a negative number equal to? For example: \sqrt{-1}^{2} It seems there are two possible ways of doing this, the problem is that I am getting two different answers using these two approaches i.e; We can first take the square of -1 and then...

I just got a new Ti-nspire Cx CAS calculator and I am having trouble with being able to express a Radical in simplified form when there are exponents and variables of x and y. My problem is that this calculator will not show the simplified form correctly. I have taken others advice in setting...

\sqrt{\frac{x-3}{x}} = \frac{\sqrt{x-3}}{\sqrt{x}} that is not true for all x, it is true for x\in [3,\infty) I want to teach my students that the exponents distribute over fractions unless we have a case like that square root or any even root. what do you think ?

1. The problem There are four charges at the corners of a square of side L. Three of the charges are -q and one is -Q(upper left corner). A) Find the force on -Q, assuming -Q< 0. B) If -Q=-q, find the electric field at the center of the square. Homework Equations Coulomb's Law E...

this is the E field above a square loop with side=a at distance z on the z axis. by symmetry the Ex, Ey field cancel out. it really kind of bothers me that I can't see this substitution, including the sin(tan^-1(u)) portion. I guess it's an easy technique but I wonder how you get the...

In Griffiths book, he says (a+ + a-)2 = a+2 + a-2 + a+a- + a-a+. Why can you NOT do the same thing for a+2 = (-ip+mωx)2 ?! When I do this to find the 2nd excited state of SHO, it gives me wrong answer. I actually have to apply a+ two times to ψ0 in order to get ψ2. It is ridiculous that...

I have some square tubing 3x3x1/4" A36 that will be fixed on one end and free on the other the material 9' long how was I find the bending moment?

Hello everyone :smile:, after spending many hours watching youtube videos, reading wikipedia articles and other related material, I came to the conclusion that my best hope at understanding this is to have an explanation personally explained to me, and I trust this is the right place to ask for...