Infinite Definition and 1000 Threads

dear all, let's consider a length L and divide it into N number of small segments uniformly. Then the length of every segment should be L/N. then we add these segments up, which is L=\sum\frac{L}{N} then we take the limit N→\infty at both sides, this means...

Homework Statement Prove that: [n+1 / n^2 + (n+1)^2 / n^3 + ... + (n+1)^n / n ^ (n+1) -> e-1 Homework Equations I have been trying it for couple of days. Tried to work the terms, natural log it all, use the byniomial theory but i can´t get to the right answer. The Attempt at a...

Homework Statement Sketch the difference of probability distributions at the two times. Does the energy change with time? The potential well suddenly disappears, what is the form of the wavefunction? Homework Equations The Attempt at a Solution Part (a) At t = 0, the probability...

What happens to ψ in a infinite potential well when the width is suddenly reduced to half its previous value ? Will this instantly adjust ψ to the new size of the well or will it take some time to confine itself in this new well ? And is there a possibility of quantum tunneling here?

Hey! :o I have to solve the following problem: $$u_t=u_{xx}, x \in \mathbb{R}, t>0$$ $$u(x,0)=f(x)=H(x)=\left\{\begin{matrix} 1, x>0\\ 0, x<0 \end{matrix}\right.$$ I have done the following: We use the method separation of variables, $u(x,t)=X(x)T(t)$. I have found that the eigenfunctions...

Hi! Here is my task: Calculate Iout if all BJT's have identical characteristics with β→∞, work on same temperature in forward active mode. Use BJT exponential transfer characteristic. Since β→∞, IB for every BJT should be zero amps and IC=IE. Equation for BJT exponential transfer...

Homework Statement Given an infinite, planar, non-conducting sheet of charge with thickness t. The volume charge density ρ is uniform. A conducting plate, held at a fixed potential V=0V, is placed parallel to the sheet at a distance d. Calculate the electric field E at all points, in all four...

Hello! How can I justify that the infinite series 1 - 1 + 1 - 1 + 1 - 1... is divergent? If I were to look at this, I see every two terms canceling out and thus, and assume that it is convergent since the sum doesn't blow up. That's what my intuition would tell me. I know I can use...

as a regular polygon increases in sides, it becomes rounder. As you increase the number of sides, the polygon will tend towards a perfect circle but never quite make it. you can only make the circle with an infinite number of sides - stopping at any other number but infinity you will only get a...

Hi Guys Could someone please point out where I'm going wrong with the following problem. If I place a magnet on a vertical surface such that the magnet must resit the force of gravity in order to hold itself in place, will this magnet stay in place forever? If it does why does this not...

So I thought up a "proof" for infinite primes. I'm assuming I did something wrong, but I don't know what, it would be nice if someone could tell me what I did wrong. Suppose there are a finite number of primes of quantity n which are listed from smallest to largest in the list: p1, p2, ... ...

Homework Statement Determine the resultant resistance of the infinite circuit made up of ##1 k\Omega## resistors shown in the figure between points A and C, and between points A and B. Homework Equations The Attempt at a Solution I can find the equivalent resistance between A...

Homework Statement Homework Equations The Attempt at a Solution I have managed to do the first 3 parts of the questions. The last two 4 markers are the ones I am having difficulties with. I have tried using the expansion postulate which states the wavefunction is equal to the...

Homework Statement Find the value of An and given that f(x) = 1 for 0 < x < L/2, find the sum of the infinite series. Homework Equations The Attempt at a Solution The basis is chosen to be ##c_n = \sqrt{\frac{2}{L}}cos (\frac{n\pi }{L}x)## for cosine, and ##s_n = \sqrt{\frac{2}{L}}sin...

Problem: If $0<x<1$ and $$A_n=\frac{x}{1-x^2}+\frac{x^2}{1-x^4}+\cdots +\frac{x^{2^n}}{1-x^{2^{n+1}}}$$ then find $\displaystyle \lim_{n\rightarrow \infty}A_n$. Attempt: I tried to see if it can be converted to a telescoping series but I had no luck. Then, I tried this: $$\lim_{n\rightarrow...

Homework Statement Part (a): Find wavefunction and energy levels. Part (b): Find a possible wavefunction. Is this wavefunction unique? Part (c): What is the probability of finding it in the ground state? Part (d): What's the probability of finding it in the second excited state? Homework...

Hi all. I'm rather a novice in the realm of physics, aside from a class in high-school and my own independent interest. I often wonder if matter is infinitely divisible. What if it's possible to divide quarks, gluons, etc, we just don't have the methods? Does anyone have input on this...

Homework Statement -I've attached a picture of the problem- An infinitely long straight wire of steady current I1 is placed to the left of a circular wire of current I2 and radius a as shown. The center of the circular wire is distance d(≥ a) away from the straight wire. Let’s find the net...

I'm reading: http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 1. In the link it says: ##2\pi\rho d\rho## is the area of the ring of the radius ##\rho## and width ##d\rho##, if ##d\rho \ll \rho##. Why is this true?? 2. A bit further down in the text it says: Since ##r^2 =...

Homework Statement A uniform linear charge of λ is located along the z axis, and concentric circular cylinder of radius 2 [m] has a surface distribution charge of α . both distributions are infinite, the distribution of linear charge is contained in the interior of the circular cylinder as...

Homework Statement 1. Consider a line of charge (with λ charge per unit length which extends along the x-axis from x=-∞ to x=0 (a) Find all components of the electric field vector at any point along the positive x-axis (b) Find the electric potential difference between any point on the...

Homework Statement I just have to graph this function to see where the "Gibbs phenomenon" occurs in its Fourier Series representation. I am pretty sure I integrated correctly.Homework Equations Fourier Series The Attempt at a Solution...

Homework Statement Show that the energy levels of a double square well V_{S}(x)= \begin{cases} \infty, & \left|x\right|>b\\ 0, & a<\left|x\right|<b\\ \infty, & \left|x\right|<a \end{cases} are doubly degenerate. (Done) Now suppose that the barrier between -a and a is very high, but finite...

Homework Statement Charge is distributed uniformly along an infinite straight line with density λ. Develop the expression for E at the general point P. Homework Equations The electric field at a point P, caused by N point charges Qi, each a distance ri from P, is given by \mathbf{E}...

Homework Statement This is for Calculus II. We've just started the chapter on Infinite Series. n runs from 1 to ∞. \Sigma\frac{1}{n(n+3)} The Attempt at a Solution I used partial fraction decomposition to rewrite the sum. \frac{1}{n(n+3)}=\frac{A}{n}+\frac{B}{n+3}...

Evaluate $\displaystyle\lower0.5ex{\mathop{\large \sum}_{n=2009}^{\infty}} \dfrac{1}{n \choose 2009}$.

Homework Statement A particle is in a bound state of the infinite square well. It is in a state represented by the following wavefunction, written here at t=0: ψ(x)= -√(2/3)√(2/L) * sin (3πx/L) + i*√(1/3)√(2/L) * sin (2πx/L) (a)Write the full time-dependent wavefunction for this state...

Homework Statement A Particle energy A trapped in infinite square well. U(x)=0 for 0<x<L and U(x)=U0 for L<x<2L. find the wave function of the particle when A) E>U0 B) E<U0 C) E=U0. Homework Equations 1-D time independent Schrodinger equation. The Attempt at a Solution I have...

Homework Statement Find a conformal mapping of the strip ##D=\{z:|\Re(z)|<\frac{\pi}{2}\}## onto itself that transforms the real interval ##(-\frac{\pi}{2},\frac{\pi}{2})## to the full imaginary axis.The Attempt at a Solution I tried to map the strip to a unit circle and then map it back to the...

Homework Statement Let \Lambda = N and set A_{j} = [j, \infty) for j\in N Then j=1 to \infty \bigcap A_{j} = empty set Explanation: x\in j=1 to \infty \bigcap provided that x belongs to every A_{j}. This means that x satisfies j <= x <= j+1, \forall j\inN. But clearly this...

Hi all. I'm having trouble understanding the cartesian product of a (possible infinite) family of sets. Lets say \mathcal{F} = \{A_i\}_{i \in I} is a family of sets. According to wikipedia, the cartesian product of this family is the set \prod_{i \in I} A_i = \{ f : I \to \bigcup_{i...

I'm not sure which category this post actually belongs to, or if the title of this post is even accurate. I guessed Calculus was the closest one. I watched this video on the web after a professor told me this mathematical phenomenon (http://www.youtube.com/watch?v=w-I6XTVZXww‎). It asserts...

Potential and wave function If a particle comes from +infinite and collides with a potential of the form : V = ∞ , x < 0 (I) -V0 , 0<x<a (II) 0 , x≥a (III) Is the wave function for region (I) = 0? And for region (II) = A sin(kx) with k constant? Really need to...

Find : $$ \sqrt{ \frac{1}{2}}\sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2}}} \sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2}}}}\sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{ \frac{1}{2} + \frac{1}{2} \sqrt{\frac{1}{2} +\frac{1}{2}\sqrt{\frac{1}{2}}}}} \cdots...

Homework Statement Compare the COMSOL results to the analytical solution for laminar flow between flat plates. Assume no effect of gravity on the flow (g = 0). The comparison will involve obtaining the velocity at a point in the flow field and the ΔP/L term. For example, you can compare the...

Homework Statement Consider steady, incompressible, parallel, laminar flow of a film of oil falling down an infinite vertical wall (Figure P-1). The oil film thickness is “h” and gravity acts in the negative Z-direction (downward on the figure). There is no applied pressure driving the flow –...

Homework Statement Determine the emf induced in the square loop in the figure if the loop stays at rest and the current in the straight wire is given by I(t)=(15.0A)sin(2500t) where t is in seconds. The distance a is 12.0 cm, and b is 15.0 cm. Homework Equations emf = Δmagneticflux/Δt...

Homework Statement I have been working on a truncated Fourier series. I have come up with a truncated series for cos (αx) and it matches my book, where in this case I'm letting x=π, and then I have shown as the book asks, Truncated series = F_{N}(π) = cos (απ) + \frac{2α}{π}...

Hello everyone! Homework Statement A charge, +q, is placed above an infinite conducting slab located at z<=0, at (0,0,d). Find the potential everywhere in space, without using the image-charge method. Homework Equations Laplace's equation(and its solution in spherical coordinates). (CGS units...

In finding solutions to the time independent Schrodinger equation we have to normalize \psi to find the constant A. So we get \int_{0}^{a} |A|^{2} sin^{2}(kx) dx = |A|^2 \frac{a}{2}=1 For A we then get |A|^2 = \frac{2}{a} . Griffiths says that this only determines the magnitude of A but...

Now you put the object right above the Earth's surface, like just a few meters above the ground. Let's just assume the object will have no gravitational affect against the Earth, or any object for that matter. It's defying logic, I know, but let's just roll with that. Assuming the object would...

Hey! :o I am lokking at the proof of the following sentence. An infinite orthonormal system $\{e_1, e_2, ... \} \subset H$, where $H$ an euclidean space, is closed at $H$ iff $ \forall x \in H$ $$||x||^2=\sum_{i=1}^n{|(x,e_i)|^2}$$ We suppose a subspace of $H$, that is produced by the basis...

Expand the quantity (t + P)^(1/2) about 0 in terms of t/P. Give four non-zero terms. (t + P)^(1/2) ~ =

This might seem like a rudimentary question but when trying to prove divergence (or even convergence) of an infinite series does the series always have to start at n = 1? For example would doing a test for \sum^{∞}_{n=1}\frac{1}{n} be any different from \sum^{∞}_{n=0}\frac{1}{n}

We have this set of primes which is infinite. This has lots of different subsets. Here is the list of subsets: Real Eisenstein primes: 3x + 2 Pythagorean primes: 4x + 1 Real Gaussian primes: 4x + 3 Landau primes: x^2 + 1 Central polygonal primes: x^2 - x + 1 Centered triangular primes: 1/2(3x^2...

It seems to me that if we consider different methods of generating a distribution of an infinite number of samples of and unbounded real number then we get some distinct results. 1) If we randomly sample a value, then its probability must be non-zero, which is also true of any other value...

Homework Statement Normalize: \Psi_1 (x,t) = N_1 \cos(\frac{\pi x}{L}) e^{-\frac{iE_1t}{\hbar}} Where N_1 and E_1 are the normalization constant and energy for the ground state of a particle in an infinite square well. Homework Equations Normalization Condition: \int_\infty^\infty P(x,t)...

Infinite potential well "proposal" Homework Statement An experimental physicist submits a proposal to a granting agency requesting support to construct an infinite potential well analogous to the one shown in Figure 3.5. Specifically, the proposal is to build a well with L = 1mm, inject some...

Question: I was just wondering if there was any error in what I've done in the following steps to find the series representation of ##lnx##. I know ## \frac {1}{x}## is given in the following link by doing having the a function centred at 0, you can let ##f(x) = ∑^∞_{n=0} \frac...

Homework Statement An infinite dielectric sheet having charge density σ has a hole of radius R in it. An electron is released on the axis of the hole at a distance R√3 from the centre. What will be the velocity which it crosses the plane of sheet? (e = charge on electron and m = mass of...