What is Infinite: Definition and 1000 Discussions

Using the boundary conditions where psi is 0, I found that k = n*pi/a, since sin(x) is zero when k*a = 0. I set up my normalization integral as follows: A^2 * integral from 0 to a of (((exp(ikx) - exp(-ikx))*(exp(-ikx) - exp(ikx)) dx) = 1 After simplifying, and accounting for the fact that...

The answer is about 40 Watts, but i am really not getting it: <Pot> = 0.5((pλ)(ωA)²)v p density linar λ wavelength ω angular frequency A amplitude v phase speed Why is this wrong? (I already tried too by <Pot> = Z*(ωA)²/2) Z is impedance

While transforming the equation of the Basel problem, the following infinite series was obtained. $$\sum_{n=1}^{\infty} \frac{n^2+3n+1}{n^4+2n^3+n^2}=2$$ However I couldn't think of a simple way to prove that. Can anyone prove that this equation holds true?

∞ ∑ (n∧2+3n+1) / (n∧4+2n∧3+n∧2) =? n=1 I attempted to find the general sum of this 'expression'?? But no luck. How can I solve this?

I am posting to ask for any comments about a couple things. I will post a link to a thread on another forum about this. and would love to hear any and all thoughts about it. the thread begins asking about 2 things. the first one is about how fast we are moving. I,402,00 mph relative to the CMB...

Find all linear differential equations of first order that satisfy this property: All solutions are asymptotic to the straight line y = 3 - x, when x -> infinity First i began writing the general equation: y' + g(x)*y = h(x) I would say that when x-> infinity, our equations will tends to 3-x...

This figure shows 2 capacitor plates. Except the region in between the 2 plates, I want to set the others as infinite elements. How to 'stretch' the x and y directions in the infinite element settings?

I remember hearing someone say "almost infinite" in this video. As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness. In this video he says that ''almost infinite'' pieces of...

I just realized quantum operators X and P aren't actually just generalizations of matrices in infinite dimensions that you can naively play with as if they're usual matrices. Then I learned that the space of quantum states is not actually a Hilbert space but a "rigged" Hilbert space. It all...

I am sure I need to use Amper's law to do that. if I use the equation I mentioned above it easy to calculate the right side of the equation but I have problem how to calculate the path integral. I know from right hand rule that the magnetic field will point at $$Z$$ and the current is in...

Hope someone can help!

We have the limit of the sequence ##\frac{a^n}{n}## where ##a>1##. I know it is ##+\infty## and i can prove it by switching to the function ##\frac{a^x}{x}## and using L'Hopital. But how do i prove it using more basic calculus, without the knowledge of functions and derivatives and L'Hopital...

Suppose you have a complex-valued function of a complex variable (namely, ##z=x+iy, \, \, x,y\in \mathbb{R}##) defined as the assumed convergent infinite product $$F(z)=\prod_{k=1}^{\infty}f_{k}(z)$$ Further suppose ##F(x+iy)=u(x,y)+i v(x,y)##, where u and v are real-valued functions. How to...

Without assuming a universal speed that is constant in all inertial reference frames, is it a necessary consequence of Galilean symmetry that interactions are instantaneous? If this is the case how can we prove this?

For all ##n\in\mathbb{N}## we have ##\emptyset \in A_n##. Hence, ##\emptyset \in \mathcal{A}_\infty##. Let ##A \in \mathcal{A}_\infty##. Then ##A \in A_k## for some ##k\in\mathbb{N}##. So ##A^c \in A_k##. Hence, ##A^c \in \mathcal{A}_\infty##. Thus, ##\mathcal{A}_\infty## is closed under...

Hi, I think I'm having a bit of a brain fart...I'm messing with this numerical code trying to understand the 1-D time-independent Schrodinger's equation infinite square well problem (V(x) infinite at the boundaries, 0 everywhere else). If normalized Phi squared is the probability of finding...

I've always had a fascination with infinite products. I like them, I do. To stimulate our ensuing conversation, I here post Knopp's two-way series-to-product (and vice-versa) "doorway" out of his book, Theory and Applications of Infinite Series pg. 226: Maybe that'll break the ice... please...

Some questions: Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well. Since we have no complex components. I am guessing that the ##\psi *=\psi##. If...

A particle of mass m is in the ground state on the infinite square well. Suddenly the well expends to twice it's original size (x going from 0 to a, to 0 to 2a) leaving the wave function monetarily undisturbed. On answering, for ##\Psi_{n}## I got ##\Psi_{n}## = ##\sqrt{\frac{1}{a}}...

Hi all, below is my attempt. Pretty new at quantum so do correct me if I'm wrong. Thanks i) Since 1nm is the wavelength of the electron, Wavelength = 1nm, 1nm=2(2nm)/n , n=4? ii) - iii) From n=1 to n=4, Change in E = 15h^2/8mL where m is the mass of electron and L is 2nm? From the change in E...

Merged thread deleted first post next post is the first post.

(NOTE: I have had a few similar postings lately on this subject, but they were much broader in scope, so I am posting only for this particular case; everything else has been figured out.) If given that limx -> a f( x ) = +∞ limx -> a g( x ) = +∞ what is the epsilon-delta formulation for...

I was looking at some websites that show the proof of addition of limits for a finite output value, but I don't see one for the case of infinite output value, which has a different condition that needs to be met - i.e., | f( x ) | > M instead of | f( x ) - L | < ε...

Hello! I am new here, and I need (urgent) help regarding the following question: Let $\boldsymbol{A}_{(n\times n)}=[a_{ij}]$ be a square matrix such that the sum of each row is 1 and $a_{ij}\ge0$$(i=1,2,\dots,n~\text{and}~j=1,2,\dots,n)$ are unknown. Suppose that...

As the temperature given was 0K, I calculated the ground state energy of the system. I considered 2 electrons to be in the n=1 state, 2 in the n=2 state and 1 in the n=3 state by Pauli's exclusion principle. By this configuration, I got the total energy of the system in the ground state to be...

In my browsing around various science forums a have come across the comment that the gravity field becomes infinite at the event horizon. I have always thought that this is a misunderstanding, and that it only becomes infinite at the central singularity. Then I found this same statement in...

Here is the image ## \tan \theta _1 = \frac{a}{z} ## ## \tan \theta _2 = \frac{a}{l+z}## where l is the length of the solenoid and z is the distance from the forward center to the point P. My doubt is how ##\theta_1## going to become 0 and ##\theta_2## ##\pi## as the length of solenoid...

I know how the math does not allow us to chose the reference point at infinity for infinite objects but I need to understand the underlying physics reason, not math reason.

I'm self studying so I just want to ensure my answers are correct so I know I truly understand the material as it's easy to trick yourself in thinking you do! A particle of mass m is in a 1-D infinite potential well of width a given by the potential: V= 0 for 0##\leq## x ##\leq## a =...

For those unaware of multifactorial notation, it should be noted that there are some common mistakes made when first being introduced to the notation. For example, ##n! \neq (n!)!## and ##n! \neq (n!)! \neq (n!)! \neq ((n!)!)!##. Just to make sure we're all up to speed, here's a quick run down...

I found that ρn = √(2n+1)/(n+1). Then, I found ρ = lim when n→∞ |(1/n) (√(2n+1))/((1/n) (n+1))| = 0 Based on this result I concluded the series converges; however, the book answer says it diverges. What am I doing wrong?

Zermelo-Fraenkel Axioms - the Axiom of Choice (ZFC), is conceptually incoherent. To me, they stole Cantor’s brilliant work and minimized it. Replies?

Consider ##f(x) = {^{\infty}x} = x \uparrow \uparrow \infty## and ##g(x)=p_{x}###, where ##p_x### is the primorial function and is defined such that ##p_n### is the product of the first ##n## prime numbers. For example, ##p_{4}### ##= 2×3×5×7=210## Let the point of intersection be defined as...

The uncountable sets [0,1] and [0,2] have the same cardinality ##2^{\aleph_0}##. Yet the second set is twice as big as the first set, in the sense of measure theory. Is there something similar for countable sets, by which we can say that the set of integers is twice as big as the set of odd...

I've read in several places that some cosmological theories posit the existence of an "infinite number of universes" with laws of physics different from our own. I'm sure there's a lot of shortcutting in the reporting and "infinite" can't really mean infinite, can it? Wouldn't an infinite number...

Attempt: I'm sure I know how to do this the long way using the definition of stationary states(##\psi_n(x)=\sqrt{\frac {2} {a}} ~~ sin(\frac {n\pi x} {a})## and ##\int_0^{{a/2}} {\frac {2} {a}}(1/5)\left[~ \left(2sin(\frac {\pi x} {a})+i~ sin(\frac {3\pi x} {a})\right)\left( 2sin(\frac {\pi x}...

The first time I saw this question I had no idea how to do it (as you can see in the figure, I lost a lot of points :s) because I was confused on how to even approach it with area of the slab from all sides being infinity. Right? That's problematic, no? Today, I just tried the problem again for...

I tried to calculate the time the charged particle will take to reach the plane using the a and using d=1/2at² and found the t to be equal to root(4εmd/σq). I guess the time period of oscillation will be double of t (by symmetry), i.e. 2root(4εmd/σq). I don't know if this is correct.

1. So for an asymptotically far-away observer, something falling towards a black hole will never reach it 2. However, the thing falling in will reach the event horizon is finite affine parameter 3. The Universe has a finite age for an asymptotically far away observer a) Does this mean that one...

After evaluating the integral I found the following: (1/3)tan-1(e∞/3) = (1/3)tan-1(∞) = (1/3)(nπ/2), where n is an odd number. In this case I found multiple solutions to the problem. How do you prove it converges?

I got the following expression: -(1/4)ln((n+2)/(n-2)) When I substitute "∞" in the expression I found it undefined. However, the book says the series converges. What am I doing wrong?

Hi, i have a question which i can't solve myself, as i am not a student of physics: I have heard of the infinite space curvature which occurs when matter collapses into a black hole. On the other hand i have heard, that a black hole radiates energy away. Now i see a contradiction: When the...

There are an infinite number of natural numbers. Why is that? Well this follows from the following facts: (i) There is at least one natural number. (ii) For each natural number there is a distinct number which is its successor, i.e., for each number $x$ there is a distinct number $y$ such that...

As I have studied before, I found that Infinite Red Shift occurs where gtt = 0 but this exercise says that on Kerr's Black Hole it doesn't really work like that. Right now I'm blocked because I didn't find anything on the internet about it so I don't know how to show this phenomenon. Any help...

Firstly, since there is no condition for the z axis in the definition of the potential can I assume that V(x,y,z) = .5mw^2z^2 when 0<x<a, 0<y<a AND -inf<z<inf? If so then drawing the potential I can see that the particle is trapped within a box with infinite height (if z is the...

Summary: No answer could be more important to the assumptions and approach to cosmology. The overwhelming bias is a finite Universe, and could this be a mistake? The measurements across the observable universe strongly indicate a Gaussian Curvature of Zero(Flat). Does this prove that Spacetime...

I have always seen this problem formulated in a well that goes from 0 to L I am confused how to use this boundary, as well as unsure of what a dimensionless hamiltonian is. This is as far as I have gotten

Hi, I have a particular equation in a paper, wherein the author specifies an infinite series. The author has apparently found the sum of the series and calculated the equation. Can anyone please help me in understanding how to sum such a series. I have attached part of the paper with the...

Hi everyone! I have started to study physics this month and I got to the Newton's laws. According to Wikipedia, the first law is: This definition made me wonder: If there was, let's say, a fictional road, infinite long and frictionless, and a body would move in constant velocity over it, could...

Hi, I'm trying to solve the sum of following infinite series: \sum_{k=1}^{\infty} \frac{{k}^{2}+4}{{2}^{k}} = \sum_{k=1}^{\infty} \frac{{k}^{2}}{{2}^{k}} + \sum_{k=1}^{\infty} \frac{4}{{2}^{k}} Using partial sum we can rewrite the first series: \sum_{k=1}^{\infty}...