Infinite Definition and 1000 Threads

In school we are taught that sunlight contains all different frequencies of light. Also that each frequency has it's own unique wavelength and energy (per photon). So my question is that if there are infinitely many different wavelengths of light (much like infinitely many numbers in an...

Homework Statement 2. Homework Equations Ohm's law and Kirchoff's voltage law The Attempt at a Solution My solution is a bit long so I will just briefly explain it. First, we find the total equivalent resistance. Since the circuit extends to infinity, it is equal to replacing the second...

The Feynman LECTURES ON PHYSICS (NEW MILLENNIUM EDITION) by FEYNMAN•LEIGHTON•SANDS VOLUME II discusses radiation from an infinite sheet of switched-on constant current in section "18-4 A traveling field" on page 18-15. The solution shows a constant E field and constant B field at a given point...

Hello Everyone. I am searching for some clarity on this points. Thanks for your help: Based on Schrodinger wave mechanics formulation of quantum mechanics, the states of a system are represented by wavefunctions (normalizable or not) and operators (the observables) by instructions i.e...

I´m not sure, whether this little challenge has been posted before. I have searched the forum and didn´t find it. It might still be a duplicate though ... Find the sum of fractions $$\frac{2}{3\cdot5}+\frac{2\cdot4}{3\cdot5\cdot7}+\frac{2\cdot4\cdot6}{3\cdot5\cdot7\cdot9}+...$$

Homework Statement Homework Equations F=ma F=Gm1m2/r2 Gauss' Law? The Attempt at a Solution I'm not sure if I should be using Gauss' Law for this question, because I've never heard of it or learned about it. I'm currently taking multi-variable calculus (gradients, vectors, etc.). From what I...

The problem I'd like to calculate the value of this sum: $$3 \sum^\infty_{k=1}\frac{1}{2k^2-k}$$The attempt ## 3 \sum^\infty_{k=1}\frac{1}{2k^2-k} = [k=t/2] = 3 \sum^\infty_{t=2}\frac{1}{2 \left( \frac{t}{2} \right)^2-\frac{t}{2}} = 3 \sum^\infty_{t=2}\frac{1}{ \frac{t^2}{2} - \frac{t}{2}} = 3...

Homework Statement When I have a disk with radius r then naturally the area is πr^2. Then I want to do this by calculus and my first step is simply taking πrdr. But the correct way is to take 2πrdr. To me this is really confusing, because I would never take 2πr dr (circumference x width)...

To find the electric field from an infinitely long charged rod you can use gauss’s law with a cylinder as your Gaussian surface. I don’t quite understand by this works. Wouldn’t the electric field given by the equation only be the electric field cause by the charge within the cylinder? And if...

Homework Statement A long wire with a current changes direction by 90 degrees. Calculate the magnetic field at the point at a perpendicular distance of S from the wire before it changed direction and a distance of T from the segment of the wire after it changed direction. Homework Equations I...

Homework Statement Calculate the electric field at point ##P## if the distance from the center of an infinitely long, charged rod to point ##P## is ##a = 0.6m##; the charge density equals ##\lambda = -CX^2##, ##C=10^{-3}C/m^3##. Show all steps in finding the equation of the field, then find the...

Hi everyone, I'm reading this paper about the solution of the heat equation inside an infinite domain: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/fourtran.pdf 1) Please let me know if the following discussion is correct. The...

How can the universe keep on expanding if it's infinite? Expanding metal, like a cube of aluminium, has a surface area which forms a border for the matter contained inside. So the universe must have a border for the matter it contains.

would that mean the Big Bang never happened? If not, please explain to the best of your ability as to why. Much appreciated.

Homework Statement First sorry for the traduction mistakes. Prove that any wave function of a particle in a 1 dimensional infinite double well of width a, returns to its original state in time T=4ma2/(πħ) . Homework Equations Ψ(x,t)=∑cnψn(x)·exp(-i·Ent/(ħ)) En=n2π2ħ2/(2ma2) The Attempt at a...

Homework Statement Homework EquationsThe Attempt at a SolutionMagnetic field due to both semi - infinite straight wires on P = Magnetic field due to infinite straight wire on P = ## \frac { \mu_0 I } { 2 \pi a } = 2 * 10 ^{-5} ~wb/m^2 ## Magnetic field due to semi – circular wire on...

Homework Statement A point charge q is located a distance d meters from an infinite plane. Determine the electric flux through the plane due to the point charge. [/B] Homework EquationsThe Attempt at a Solution I consider another infinite plane at a distance d in the opposite direction. Now I...

1. The problem statement, all variables andgiven/known data Know how to find energy levels in infinite wells Homework Equations Good Question Is it: n^2h^2/8mL^2 3. The Attempt at a Solution So I am taking a test later today, and it was brought to my attention "know how to find energy levels...

Hi, I'm studying the "Child Langmuir law". We have a grounded cathode that is an infinite plane with free electrons, and an anode with a positive voltage V. The text says that the current density J is constant between the two plates for the "Charge conservation principle". I was not able to...

Homework Statement On the axis of an infinite wedge that moves with velocity ##\vec{V}##, the body decays with the formation of a lot of splinters that fly away uniformly in all directions with velocity ##\vec{u}##. What should be the angle of the wedge that half of the splinters fall on its...

Couldn't really fit the precise question in the title due to the character limit. I want to know what are some sufficient conditions for a model in classical field theory to possesses infinitely many conserved quantities. The sine-Gordon and KdV equations are examples of such systems. Now...

I want to show that the function defined as follows: $f(x)=e^{-1/x^2}$ for $|x|>0$ and $f^{(k)}(0)=0$ for $k=0,1,2,\ldots$ is infinitely differentiable but not analytic at the point $x=0$. For infinite-differentiability I used the fact that $\lim_{|x|\to 0^+} x^{-n} e^{-1/x^2}=0$ for every $n$...

I came across the following argument that attempts to show that the notion of infinite decimal numbers is incoherent. Try adding these two numbers:05.4123482100439884... 16.3482518100560115... ___________________ 21.760600020?999999...By the Axiom of Choice, "There exist arbitrary infinite...

Sorry if this has been answered already, i searched for a while. I know how to solve the problem of the potential of a point charge near a grounded infinite conducting plane, and a line charge near an infinite conducting plane. If the plane isn't necessarily grounded, say its at some potential...

Given is the function f: R2 -> R, with f(x,y)=x2+y2-6xy+8y. The level surface f(x,y)=1 contains infinitely much points (x,y) where x and y are integer. How can I prove this? I see that it is true with some examples, but how can I prove this. Do I need to use the gradient? Or tangent planes? Or...

I'm trying to make an approximation to a series I'm generating; the series is constructed as follows: Term 1: \left[\frac{cos(x/2)}{cos(y/2)}\right] Term 2: \left[\frac{cos(x/2)}{cos(y/2)}-\frac{sin(x/2)}{sin(y/2)}\right] I'm not sure yet if the series repeats itself or forms a pattern...

I've read that it is unsatisfactory to consider infinitely many basis vectors to span an infinite dimensional space. For example, for the infinite dimensional Hilbert space, {e1,e2,e3...} we could use this to make an arbitrary infinite tuple (a,b,c,...). If this is looked down upon, then why are...

Gluing Lemma: Let X be a topological space, and suppose X = A_1 U A_2 U ... U A_k, which each A_i is closed in X. For each i, let f_i: A_i ---> Y be a continious map s.t f_i = f_j on the intersection of A_i and A_j. Then the book goes on to give an example of where this is not true for an...

Homework Statement I have a few questions I'd like to ask about this example. (C1 was already derived before the second part) 1. What does the line "The rest of the coefficients make up the difference" actually mean? 2. What does "As one might expect...because of the admixture of the...

I have read some of the other posts about this topic but am still left unsatisfied. Could just be me. :cool: Did the universe, one minute after the big bang, consist of a finite volume of spacetime? If so, then is it not logically inconsistent that the universe can possibly be infinite now...

Homework Statement In the layer ##0<z<a## there is a uniform and constant density of charge ##\rho>0##. In the layer ##-a<z<0## the density of charge is ##\rho<0##. What is the total electric field in the space?The Attempt at a Solution By the Gauss law I find that if ##z \geq a## or ##z \leq...

I was recently charging my phone and I plugged it out when it reached 94%. I have been using it for over an hour now, and it still says it is charging and the battery still is at 94% This is amazing!

My thoughts are concerning an infinite sheet carrying current in a direction. I wish to induce a unidirectional electric field outside of the sheet via induction. My ideas were that if the current was changed linearly in a sawtooth fashion, then I would achieve the induced electric field in...

Homework Statement Referencing image attached. I'm not sure how the example arrived at ψ ⇒ 0 at x<0 and >L as K ⇒ ∞ in the limiting case of an infinite potential well. Homework EquationsThe Attempt at a Solution I tried simply applying limits to the wavefuction but in the case x<0, the...

Suppose set A is defined as the even integers and set B is defined as for every even integer there are two odd integers, like so: {2,3,3,4,5,5,6,7,7 ... } Can you calculate that the probability of choosing an odd number is 66%?

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] I have drawn this diagram using MS paint, could you please tell me some other software in which I can draw and insert greek symbols, too ?Let me take the origin at O. ## \hat r \left(\alpha\right) ≡ \hat r\text{ at...

This question on quora discusses whether an infinite universe would allow for a repetition of patterns and arrangements of matter. The top answer gives a very convincing argument as to why this would be impossible because, he reasons, that spacetime is causally connected. However if the universe...

An electron can tunnel between potential wells. Its state can be written as: $$ |\psi\rangle=\sum^\infty_{-\infty}a_n|n\rangle $$ Where $|n \rangle$ is the state at which it is in the $n$th potential well, n increases from left to right. $$...

Wouldn't the first thought be that we would be burned to a crisp if we where hit with all the light(in our path) across the span of the entire universe simultaneously? It seems there could be paradoxes even before the advent of relativity. Or maybe it was shown mathematically that the energy...

According to this page: https://en.wikipedia.org/wiki/Cantor's_theorem It says: "Cantor's theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself." Furthermore, it says: "Cantor's...

Homework Statement An infinite non-conducting plate of thickness ##d## lies in the ##xy## plane. The bottom surface of the plate lies in the plane ##z=0##. The charge density of the plate is ##\rho=\rho_0 z /d~,~\rho_0>0##. Find the electric field in the regions ##z<0~~,~~0<z<d~~,~~z>d## and...

Homework Statement Trying to find the sum of (-1)3n+1/(2n-1)3. by using term-by-term integration on the cosine Fourier series x= L/2-4L/π2∑cos(((2n-1)πx)/L)/(2n-1)2. Homework Equations Shown below The Attempt at a Solution When integrating and substituting Lx/2 for x's sine Fourier series I...

I wavered in the past from starting a thread on this subject because I thought it would break some rules but I think if I word it correctly, there should be no problem. You know how this goes. The Universe cannot be eternal because, irrespective of what new physics we learn, an eternal Universe...

I'm trying to get the eigenfunctions and eigenvalues (energies) of an infinite well in Python, but I have a few things I can't seem to fix or don't understand... Here's the code I have: from numpy import * from numpy.linalg import eigh import matplotlib.pyplot as plt from __future__ import...

It is required to be continuous in the following text: The book's reason why wave functions are continuous (for finite V) is as follows. But for infinite V, ##\frac{\partial P}{\partial t}=\infty-\infty=## undefined, and so the reason that wave functions must be continuous is invalid...

Find derivative of y=✓{x+✓[y+✓(x+...)]}infinite. Here root comes for total inter terms

I'm familiar with the relationship \nabla\cdot\frac{\hat{r}}{r^2}=4\pi\delta(r) in classical electromagnetism, where \hat{r} is the separation unit vector, that is, the field vector minus the source vector. This is result can be motivated by applying the divergence theorem to a single point...

Homework Statement Every infinite cyclic group has non-trivial proper subgroups Homework EquationsThe Attempt at a Solution I know that if we have a finite cyclic group, it only has non-trivial proper subgroups if the order of the group is not prime. But I'm not sure how to make this argument...

find the sum of this infinite geometric series: 1 - √2 + 2 - 2√2 + ... a.) .414 b.) -2.414 c.) series diverges d.) 2 I found that the common difference is 2, so I calculated this: S∞= -.414/-1 s∞= .414 So i got that the answer is A, but will you check this?

Homework Statement A particle of mass m is moving in an infinite square well of width a. It has the following normalised energy eigenfunctions: $$u_n (x) = \sqrt{\frac{2}{a}} sin(\frac{n \pi x}{a})$$ (1) a) Give an expression that relates two orthogonal eigenfunctions to each other and use it...