What is Infinite: Definition and 1000 Discussions

Homework Statement Consider a sequence of non negative integers x1,x2,x3,...xn which of the following cannot be true ? ##A)\sum ^{\infty }_{n=1} x_{n}= \infty \space and \space \sum ^{\infty }_{n=1} x_{n}^{2}= \infty## ##B)\sum ^{\infty }_{n=1} x_{n}= \infty \space and \space \sum ^{\infty...

Homework Statement At t < 0 we have an unperturbed infinite square well. At 0 < t < T, a small perturbation is added to the potential: V(x) + V'(x), where V'(x) is the perturbation. At t > T, the perturbation is removed. Suppose the system is initially in the tenth excited state if the...

A particle is in its ground state of an infinite square well of width a <xl i>=√2/a*sin(πx/a) and since it's an eigenstate of the Hamiltonian it will evolve as <xlα(t)>=√2/a*sin(πx/a)e^(-iE1t/ħ) where E=π2ħ2/2ma2 If the well now suddenly expands to witdh 2a If the well suddenly expands to 2a...

Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?

Suppose we have a "particle" which can be at some position x∈N (where N={0,1,2,...}). The probability that the particle is at position x can be written as: P(x) = 1/(2x+1) Now suppose we have two particles p1 and p2.To keep things simple, assume that the individual probability distribution for...

Hey guys! I just have a question regarding finding the sum of an infinite series. Attached is the image of the question. I've tried to use the ratio test but it doesn't give me the result I need which happens to be 1/sqrt(2). I feel like this is one of those power series questions, but I'm not...

Homework Statement The cylinder has a radius a and is perpendicular to the electric field, E(r)=E(x_hat). It also carries charge Q. The potential is of the form V(r,φ)=A0+A0'ln(r)+∑(n=1 to ∞)((Ancos(nφ)+Bnsin(nφ))rn+(An'cos(nφ)+Bn'sin(nφ))r-n) Homework Equations V=-∫E⋅dl The Attempt at a...

given all the great minds of physics, i still have trouble with this one. "the uverse is infinitely big" and "the uverse is expanding" my understanding is you can't have both, because to define expansion you need measurable differential on a boundary, thus expansion by definition infers...

Hello there. I'm here to request help with mathematics in respect to a problem of quantum physics. Consider the following function $$ f(\theta) = \sum_{l=0}^{\infty}(2l+1)a_l P_l(cos\theta) , $$ where ##f(\theta)## is a complex function ##P_l(cos\theta)## is the l-th Legendre polynomial and...

I want to solve the Poisson equation for a thin slab of charge held above a grounded plane at z=0. The problem is somewhat reminiscent of the classical image problem of a point charge above an infinite grounded plane but differs because we are using a slab of charge instead which extends above...

If stars have finite mass, gravity, and density, why does a black hole have infinite density, mass, and gravity and why doesn't it attract everything around it with such infinite gravity? Also, with infinite density, why are black holes all different sizes?

Homework Statement A particle of mass m, is in an infinite square well of width L, V(x)=0 for 0<x<L, and V(x)=∞, elsewhere. At time t=0,Ψ(x,0) = C[((1+i)/2)*√(2/L)*sin(πx/L) + (1/√L)*sin(2πx/L) in, 0<x<L a) Find C b) Find Ψ(x,t) c) Find <E> as a function of t. d) Find the probability as a...

The reason why I have this question is because I’ve been thinking that the observable universe is filled with galaxies and planets mostly around stars , and we also have explored that there are a lot of black holes in the universe which if I’m correct are simply dead stars which once had energy...

Just googled, "Is the universe infinite?" and got this: "The surface of the torus is spatially flat, like the piece of paper, but finite. However, with expansion, it is possible that even if the universe just has a very large volume now, it will reach infinite volume in the infinite future."...

Most than a question, I'd like to show you what I've got to understand and I want you to tell me what do you think about it. I'm not a math expert, I just beginning to study maths, and I'm reading Elements by Euclids, and I've been doing some research on immeasurable numbers. My statement is...

Homework Statement Hello, I am currently doing some holiday pre-study for signals analysis coming up next semester. I'm mainly using MIT OCW 6.003 from 2011 with some other web resources (youtube, etc). The initial stuff is heavy on the old infinite series stuff, that seems often skimmed...

Homework Statement This is problem 17 from Chapter 3 of Quantum Physics by S. Gasiorowicz "Consider the eigenfunctions for a box with sides at x = +/- a. Without working out the integral, prove that the expectation value of the quantity x^2 p^3 + 3 x p^3 x + p^3 x^2 vanishes for all the...

Homework Statement Find the sum of the following series: $$ \left( \frac 1 2 + \frac 1 4 \right) + \left( \frac 1 {2^2} + \frac 1 {4^2} \right) +~...~+ \left( \frac 1 {2^k} + \frac 1 {4^k} \right) +~...$$ Homework Equations $$ \sum_{n = 1}^{\infty} \left( u_k+v_k \right) = \sum_{n =...

[Please excuse the screengrabs of the fomulae - I'll get around to learning TeX someday!] 1. Homework Statement Find the sum of this series (answer included - not the one I'm getting) The Attempt at a Solution So I'm trying to sum this series as a telescoping sum. I decomposed the fraction...

Homework Statement A fishery manager knows that her fish population naturally increases at a rate of 1.4% per month, while 119 fish are harvested each month. Let Fn be the fish population after the nth month, where F0 = 4500 fish. Assume that that process continues indefinitely. Use the...

If the universe is indeed flat and the cosmological principle holds true, does this mean that there is an infinite amount of space in the universe as well as an infinite amount of matter?

Hello! I'm doing a school project, where I am writing about Infinity in Math and Physics. I've got the math part settled, but it's the physics part that has begun to bother me. One part of my task is to write about some of the mathematical expressions in physics, where we use infinity - but the...

I read some time ago a resume of the book the Crack In The Cosmic Egg and this is more or less what it told: When a rocket acquires light speed its mass becomes infinite which creates a gravity force field that crunches all the universe making it restart. Its argued that to propel a rocket to...

Homework Statement An infinite line of charge with charge density λ is parallel to and a distance d above an infinite grounded conducting plate. What is the charge density σ that is induced in the plate? For simplicity, consider the line of charge to lie along the line x = 0. Homework...

Suppose $G$ is an infinite group and $H$ is an infinite subgroup of $G$. Let $g\in G$. Suppose $\forall h\in H\ \exists h'\in H$ such that $gh=h'g$. Can we conclude that $gH=Hg$? What if $G$ and $H$ are of finite orders?

...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?

Homework Statement Balance :- $${Cl_2O_7} + {H_2O_2} {\longrightarrow} {ClO_2^-} +{O_2} + {H^+}$$ Medium :- basicHomework EquationsThe Attempt at a Solution $${\stackrel{+7}{Cl_2}\stackrel{-2}{O_7}} + {\stackrel{-1}{H_2}\stackrel{-1}{O_2}} {\longrightarrow}...

Find the surface in terms of a,b,c on which the following system of equations has no solution ax-2y+3z=5 -x+y-bz=-3 2x+cy-2z=d Could there be any values of a,b,c,d for which the system has infinite solution? (Justify).

Hi.. I am stuck up with a double integration where one of the integration limit is infinity. I know quadpack (qagi) can handle integration over infinite intervals. But how to make it work for the double integration. Or if there is any other routine that can handle both double integration and...

Can x/(z+y) be written as an infinite sum?

I could've peeked at the solution manual and end with it at that. However, I'm trying to change this nasty habit and solve this problem myself. I might be too ambitious. Here goes. Homework Statement Consider the infinite Atwood's machine shown. A string passes over each pulley, with one end...

It seems to me that convergence rounds away the possibility of there being a smallest constituent part of reality. For instance, adding 1/2 + 1/4 + 1/8 . . . etc. would never become 1, since there would always be an infinitely small fraction that made the second half unreachable relative to the...

Homework Statement A particle is in the n=1 state in an infinite square well of size L. What is the probability of finding the particle in the interval Δx = .006L at the point x = 3L/4? Homework Equations ψ(x) =√(2/L) sin(nπx/L) The Attempt at a Solution The problem states that because Δx is...

Homework Statement Find the sum of the given infinite series. $$S = {1\over 1\times 3} + {2\over 1\times 3\times 5}+{3\over 1\times 3\times 5\times 7} \cdots $$ 2. Homework Equations The Attempt at a Solution I try to reduce the denominator to closed form by converting it to a factorial...

Question ∞ ∑ tan(1/n) n = 1 Does the infinite series diverge or converge? Equations If limn → ∞ ≠ 0 then the series is divergent Attempt I tried using the limit test with sin(1/n)/cos(1/n) as n approaches infinity which I solved as sin(0)/cos(0) = 0/1 = 0 This does not rule out anything and I...

I have a set of data that I've been working with that seems to be defined by the sum of a set of exponential functions of the form (1-e^{\frac{-t}{\tau}}). I've come up with the following series which is the product of a decay function and an exponential with an increasing time constant. If this...

Hi folks, I was wondering if there are books that explain how to solve differential equations using infinite series. I know it is possible to do it since Poincaré used that method. Do you know which ones are the best? I find books on infinite series but they talk just about series...

Homework Statement A thin infinite wire with linear charge density λ is located parallel to an infinite conducting surface, which is coincident with the x-y plane (i.e., z = 0). The wire is parallel to the ˆx direction and is located a distance z = d from the conducting surface. The figure on...

Homework Statement We just started capacitors in class and we were introduced to the formulae q=CV and i = C*dV/dt In the notes it said that if the voltage across a capacitor were to change instantenously, the capacitor current would be infinite. It goes on to say why this is never possible...

Homework Statement Determine what colors of visible light would be absorbed by electrons in an infinite well, N = 3.1 nm. The effective mass for an electron in GaAs is one-fifteenth of the standard electron mass. Homework Equations En = πh2/[2*N2*me/15]*n2 L = nλ/2 Ψ = √(2/L)sin(nπx/L) The...

Homework Statement ISW walls at 0 and L, wavefunction ψ(x) = { A for x<L/2; -A for x>L/2. Find the lowest possible energy and the probability to measure it? Homework Equations Schrodinger equation ψ(x)=(√2/L)*(sin(nπx/L) cn=√(2/a)∫sin(nπx/L)dx {0<x<a} En=n2π2ħ2/2ma2 The Attempt at a...

Homework Statement Write a program to find the equivalent resistance between two opposite corners within a grid of "infinite size" with resistors between each point. So basically we have an infinite cube made up of cubes with 1 ohm resistors between each node. Homework Equations Kirkoff's laws...

I apologize in advance for not being familiar with LaTex. 1. Homework Statement One thousand neutrons are in an infinite square well, with walls x=0 and x=L. The state of the particle at t=0 is : ψ(x,0)=Ax(x-L) How many particles are in the interval (0,L/2) at t=3? How many particles have...

Hello, Reading Richard Feynman’s book “Quantum Electrodynamics” (Edited by Advanced Book Classics), I read that the electron’s self-energy is infinite and that has been a trouble for QED during 20 years. Feynman proposed a solution based on a cut-off, but that’s not fully satisfactory and I...

Homework Statement Use Eisenstein's criterion to show that there exists irreducible polynomials over Q or arbitrarily large degree, and from this deduce that the field of algebraic numbers is an infinite extension of Q Homework Equations none The Attempt at a Solution Note that x^n+4x+2 is...

And virtual particles potential energy is infinite too? As more and more dark energy is created does this mean that the potential energy of dark energy is infinite? Does that happen for virtual particles in vacuum and vacuum energy too?

https://en.m.wikipedia.org/wiki/Vacuum_energy And it is this type of energy dark energy or a form of it?

Homework Statement To Determine Whether the series seen below is convergent or divergent. Homework Equations ∑(n/((n+1)(n+2))) From n=1 to infinity. The Attempt at a Solution Tried to use the comparison test as the bottom is n^2 + 3n + 2, comparing to 1/n. However, this does not work as the...

1. ##<x>= \int_{0}^{a}x\left | \psi \right |^{2}dx## ##\psi (x)=\sqrt{\frac{2}{a}}\sin\frac{n\pi x}{a}## then ##<x>= \frac{2}{a} \int_{0}^{a}x \sin\frac{n\pi x}{a}dx## 2. Homework Equations 1) ##y=\frac{n\pi x}{a}## then ##dy=\frac{n\pi}{a}dx## and 2) ##y=\frac{n\pi x}{a}## then...

This is about the legitimacy of a possible operation. Take 0.999999... The operation is defined like this: 1) identify the insertion position with respect to the decimal. in this example we choose "3" as in the third position, 0.999999... 2) from the insertion position, inclusive, to the...