Infinite Definition and 1000 Threads

Assuming the most common Dark Energy models, it's density remains constant even with the universe expansion. As new space volume is created, it contains the same amount of dark energy as the previously existing space for the same volume unit. If we assume that at a certain epoch of cosmic time...

It is well known that the below series are divergent $1 - 1 + 1 - 1 + \cdots $ $1 - 2 + 3 - 4 + \cdots $ $1 + 2 + 3 + \cdots $ But after i watched a video in youtube for the channel " Numberphile " they proved that the first is equal to 1/2 , 1/4 and the last one is -1/12 ! The way to...

It is known that a non-conducting sheet of charge (charge on only one "side") has electric field magnitude $$E=\frac{\sigma}{2\varepsilon_0},$$ where $\sigma$ is the surface charge density in Coulombs per square meter. Suppose now that we have an infinite sheet, but it has a thickness $\ell$ to...

If we suppose universe is infinite than there will be no parallel universes.So I know that If ##Ω_k##→Universe will be infinite.Then there will be no parallel universes cause there's one universe. I am confused.Is that mean the parallel universe idea is wrong ?

Homework Statement I am working on a problem that states the following: Imagine an infinite straight wire carrying a current I and uniformly charged to a negative electrostatic potential Φ I know here that the current I will set up a magnetic field around the wire that abides to the right...

I need some help in optimizing a code with a prompt yes/no...My problem is that if I mistype within the loop for r some character (let's say I'm missing the number 8 on the keyboard for u) the program gets into an infinite loop. Do you know some way that I could solve this problem? Like printing...

Homework Statement Work out the variance of momentum in the infinite square well that sits between x=0 and x=aHomework Equations Var(p) = <p2> - <p>2 $$ p = -i\hbar \frac{{\partial}}{\partial x} $$ The Attempt at a Solution I've calculated (and understand physically) why <p> = 0 Now I'm...

Is that true every event has %99.99 chance to occur eventually if the time is infinite ?

I need some help from people who can read the math in papers by such physicists as Linde. In his 2014 paper (on the web) "Inflationary Cosmology after Planck 2013", he says, "False vacuum is a metastable state without any fields or particles but with large energy density. Imagine a universe...

Hey everyone, I'm currently in Calc 2 and the only thing I seem to be having a problem with is a couple of the convergence tests. When I take pretty much any math course, I always use mathematica to help check my answers when I'm doing HW or practicing so I don't waste time. My question is...

Homework Statement Consider an infinite square well defined by the potential energy function U=0 for 0<x<a and U = ∞ otherwise Consider a superposed state represented by the wave function ## \Psi(x,t)## given at time t=0 by $$\Psi(x,0) = N \{(-\psi_1(x) + (1+ i)\psi_2(x)\}$$ 1. Assume that...

Homework Statement An asteroid which strikes the Earth starts from rest a very large distance r from the Earth (say r = ∞). What will its speed be when it hits the earth? (Use M = 6.0×1024 kg, r= 6.4×106 m, G = 6.7×10-11 m3 kg-1 s-2) Homework Equations [/B] U=-GmM/r F=GmM/r^2 The Attempt...

Would someone like to have a conversation with me about the bounds of the universe and energy? I have a few ideas rambling around.. When I say bounds I mean the expanding bubble. But I would like to discuss infinite matter and infinite energy big crunch possibility. I'm a beginner with BIG thoughts.

Homework Statement Homework Equations The Attempt at a Solution a) For this part, I know for distinguishable particles, the expectation value of the square distance $$\langle (x_{1}^{2} - x_{2}^{2}) \rangle = \langle x^{2} \rangle_{2} + \langle x^{2} \rangle_{3} - 2 \langle x \rangle_{2}...

1. The problem statement, all variables a nd given/known data A rectangular trough extends infinitely along the z direction, and has a cross section as shown in the figure. All the faces are grounded, except for the top one, which is held at a potential V(x) = V_0 sin(7pix/b). Find the...

The closure relation in infinite dimension is : ∫|x><x|dx =I (identity operator),but if we apply the limit definition of the integral the result is not logic or intuitive. The limit definition of the integral is a∫b f(x)dx=lim(n-->∞) [i=1]∑[i=∞]f(ci)Δxi, where Δxi=(b-a)/n (n--.>∞) and...

The ground state energy of a particle trapped in an infinite potential well of width a is given by (ħ2π2)/2ma2. So the momentum is given by (2mE)1/2 = ħπ/a. Since this is a precise value, doesn't that mean that we know momentum with 100% certainty? And if that is the case shouldn't the...

Homework Statement Determine whether the series is converging or diverging Homework Equations ∞ ∑ 1 / (3n +cos2(n)) n=1The Attempt at a Solution I used The Comparison Test, I'm just not sure I'm right. Here's what I've got: The dominant term in the denominator is is 3n and cos2(n)...

Hello, I heard that theoretical particles that have negative mass (techyons) are predicted to tend to speed up to infinite, if their energies are low enough. I don't understand why infinite speed instead of 2c (double the speed of light) are predicted? Note: I don't know whose/which theory it...

Homework Statement Here is the problem I am stuck on. I have checked my process multiple times, but have come up with the same wrong result. I would like to find out where by error of thinking lies. "An infinitely long line charge of uniform linear charge density λ = -1.30 µC/m lies parallel...

Homework Statement I have this exercise: Calculate ##\sum\limits_{k=0}^\infty t^{k}sin{(kx)}## Where x and t are real and t is between 0 and 1. Homework Equations ? The Attempt at a Solution The ratio test says that this sum does have a limit, and tk obviously converges, as t is between 0 and...

When modelling the heat transfer through a plate using fouriers equation, what difference would it make if the width and length of the plate were set to a specified value rather than being infinite?

We have learned the below formula for a plane sheet of charge with thickness. E=σ/ϵ and the one below for with no thickness (negligible) E=σ/2ϵ The problem, I am facing is digesting the derived equations. It is one thing for sure that these formulas must be right. But then the fact that E...

While I'm reading a book in quantum mechanics, I reached the part "Generalization to infinite dimension". We know that at infinite dimension many definitions changes.And that what is confusing me! Take for example the inner product.when we are dealing in finite dimension the definition of inner...

Olbers' paradox reckons that the sky should be blazing bright if there is an infinite number of evenly distributed stars (galaxies). the argument is something like in every direction that you look there would be a star. so the sky would be blazing bright. but even if there were an infinite...

The following question came up when me and a friend of mine were discussing some basic things about probability:Let $p$ be a real number in $[0,1]$. Does there exist a sequence $(x_1, x_2, x_3, \ldots)$ with each $x_i$ being either $0$ or $1$, such that $$ \lim_{n\to \infty} \frac{f(n)}{n} =p...

In their admirably bold Dec. 2014 paper "Cosmology from quantum potential", Ali and Das claim that a reformulation of General Relativity, using Bohmian quantal trajectories in place of geodesics, tentatively confirms that the universe is of infinite age and had no beginning. I'm grateful to...

Homework Statement A particle of mass m is confined to a space 0<x<a in one dimension by infinitely high walls at x=0 and x=a. At t=0, the particle is initially in the left half of the well with a wavefunction given by, $$\Psi(x,0)=\sqrt{\dfrac{2}{a}}$$ for 0<x<a/2 and, $$\Psi(x,0)=0$$ for a/2...

Homework Statement Find the electric field between the conductor and ground. The conductor is at: Potential = +V0, radius a distance d from the ground plane. Homework Equations I used image theory to create a conductor at -V0 at distance -d from the ground plane. Laplace's equation: ∇2V = 0...

How do you show that $$\frac{1}{z}\prod_{n=1}^\infty \frac{n}{z+n}(\frac{n+1}{n})^z$$ is meromorphic? Any hints would be helpful, I'm having trouble bounding the functions and their logarithms. This is exercise XIII.3 problem 15 in Gamelin's Complex Analysis.

I've just encountered the infinite series ## \sum_{n=0}^\infty n e^{-n\lambda} ##. I know that in general its not possible to evaluate an infinite series but because wolframalpha.com could evaluate it(which gave the result ## \frac{e^{\lambda}}{(e^\lambda-1)^2} ##), it seems to me that this one...

Alright I'm a noob to all this but I have been reading a really good book that talks about special relativity and had a question. Considering that light does not pass through time, it travels between any two points in zero time, correct? Does that mean that from the perspective of the light...

I am trying to determine the size of a conductive 2-D sheet that has a specified degree of increased resistance (or reduced conductivity) compared to an infinite sheet. Imagine that electrons enter the infinite sheet and exit the sheet at 2 points which are 1 unit of distance apart and aligned...

In my EM book, Wentorth, he used the example of a transmission line as an infinite line of charge. The book states "...a test charge placed a couple of centimeters from an elevated transmission line will see what appears to be an infinite length line (of charge)." I'm confused why this would...

Homework Statement I came across a problem where f: (-π/2, π/2)→ℝ where f(x) = \sum\limits_{n=1}^\infty\frac{(sin(x))^n}{\sqrt(n)} The problem had three parts. The first was to prove the series was convergent ∀ x ∈ (-π/2, π/2) The second was to prove that the function f(x) was continuous...

Evaluate the infinite series $1-\dfrac{2^3}{1!}+\dfrac{3^3}{2!}-\dfrac{4^3}{3!}+\cdots$.

Dear Physics Forum, Is the Uncertainty Principle the cause of the infinite solutions to Schrodinger's equation? I get the sense it is not. Could you elaborate a little? Thanks, Mark

Homework Statement Homework EquationsThe Attempt at a Solution (a) $$ \int_{0}^{a} \mid \Psi (x,0) \mid^{2} \hspace {0.02 in} dx = 1 $$ $$ \int_{0}^{a} \mid A[ \psi_{1}(x) + \psi_{2}(x) ] \mid^{2} \hspace {0.02 in} dx = 1 $$ Since the ##\psi_{1}## and ##\psi_{2}## are orthonormal (I don't...

Hey, Just wanted to thank everyone for their time to help solve people problems, I can generally find all my answers here but I made an account now because i can't seem to find a related problem to this. In general the textbook for these types of problems make the plane z=something. In this...

If the Singularity Has Infinite Mass, How Does Merging With Another Black Hole Create "Suoermassive" Black Holes? Infinite Plus Infinite Is Infinite. No Increase.

I know the solution has an infinite number of solutions. It is represented as follows: x1= 4/3 + (1/3)x3 - (5/3)x4 x2= 2 + (1/3)x3 + (1/3)x4 x3= Free x4= Free How do I put the above solution into vector form as illustrated in the original question?

Homework Statement Consider an infinitely long solid cylinder of uniform linear charge density λ1 and radius a inside a hollow cylindrical pipe of inner radius b and outer radius c and uniform linear charge density λ2. A cross-sectional view of the system is shown below(linked and attached)...

Homework Statement So the equipotential surface of a point charge is sphere with the charge in the center, and the equipotential surface of a infinite line is a cylinder with the line of charge as the axis. I was wondering what is the shape of the equipotential surface of a infinite plane...

Homework Statement I am trying to solve a problem from Jackson's book (in chapter 8). I must describe the propagation of a TEM mode through a transmission line that consists of two infinite conductor plates that are parallel to each other and separated by a distance a. There's a dielectric...

Homework Statement The bottom of an infinite well is changed to have the shape $$V(x) = \epsilon \sin {\dfrac{\pi x}{b}}, 0 \le x \le b$$ Calculate the energy shifts for all the excited states to first order in ##\epsilon##. Note that the well originally had ##V(x) = 0## for ##0 \le x \le...

Homework Statement An infinite wire carries current I. I hope the picture works! The vertical arrow shows the direction of current in the wire. The green arrow has length a and ends at point P. What is the magnitude of the magnetic field at point P? Homework Equations dB = (μ/4π) (I dl×r...

Please help! I read a statement by Lee Smolin (Time Reborn) that an "open" infinite universe necessarily has a "boundary", through which information would be received, which he used as an argument that cosmological models should prefer a "closed" universe approach. In fairness, he said that this...

Homework Statement Part a.) For a>0 Determine Limn→∞(a1/n-1) Part b.) Now assume a>1 Establish that Σn=1∞(a1/n-1) converges if and only if Σn=1∞(e1/n-1) converges. Part c.) Determine by means of the integral test whether Σn=1∞(e1/n-1) converges Homework Equations Integral Test Limit...

A person asked this question of me recently and it generated some discussion amongst the people in the room (many of whom had a limited background in physics). The original question went something like this: suppose that a ball is initially at rest in a wagon and the wagon is given a horizontal...

A theorem on equivalence relation states that for any set S, the set of equivalence classes of S under an equivalence relation R constitutes a partition of a set. Moreover, given any partition of a set, one can define an equivalence relation on the set. What allows you to "create" a partition...