Finite Definition and 1000 Threads

Homework Statement I'm trying to derive an analytical expression for the photon backscatter flux in finite turbid media using the diffusion equation and the method of images. What I want to write is: for a given volume (x,y,z), where a coherent light source is incident on the x-y plane and z is...

speed? This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky. In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite...

The universe- from our understanding, is expanding, thus the regions (for lack of a better word) particles have not yet reached do not exist. How far our universe can/ will expand is unknown, it may be infinite, but we can conclude at this time, as it is still expanding, that it is finite. True...

I am assuming scientists say that the universe is 13.8 billion years old with respect to time on earth. If so, how come the infinite energy present at such a small scale didn't make gravitational time dilation infinite during the first stage? Wouldn't time dilation make the universe infinitely...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

I am reading Paul E. Bland's book "Rings and Their Modules ... Currently I am focused on Section 2.2 Free Modules ... ... I need some help in order to fully understand Bland's Example on page 56 concerning directly finite and directly infinite R-modules ... ... Bland's Example on page 56...

I'm trying to numerically solve the time dependent Schrödinger equation and I've been told that the best approach is to numerically integrate using a finite difference method, however I don't understand why I couldn't just use ode45 to solve it?! Is the finite difference (interpolation) method...

I found this part of forum the most relevant to this theme so excuse me if I missed. This year I'm doing a high school summer project related to quantum mechanics. Anyway I'm using finite difference method to solve Schrodinger equation. Before starting to work on a project I decided to get some...

OK, so it's time to start a new thread. I heard many times that there exists only one black hole solution for a given mass and angular momentum, but I know already that this is not true. We all know that if we throw something into an existing black hole, its event horizon starts to ripple. So...

Homework Statement Comment how the energy and wave functions of the electron would change in the case of a finite dept quantum well with the same width. Homework EquationsThe Attempt at a Solution I feel completely clueless as how to approach! :( * The full question can be found in the...

I've calculated the eigenstates of the Hubbard Hamiltonian for two fermions. The ground state is (U2 - (U2 + 16t2)1/2)/2 For U = infty, I get 0. For U >> t, I should get the exchange energy J = -4t2/U How do I get from the ground state equation to J?

Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that...

Q7. Name an extension of \(\mathbb{Q}\) over which \(\pi\) is algebraic of degree 3. I have a very simple answer to this (below) but is it correct? Is it likely to be what the text is after? \(\mathbb{Q}(\pi^3)\) is an extension of \(\mathbb{Q}\), it is not an algebraic extension but I am not...

Homework Statement A string of length L =8 is fixed at both ends. It is given a small triangular displacement and released from rest at t=0. Find out Fourier coefficient Bn. Homework Equations what should i use for U0(x) ? The Attempt at a Solution

Homework Statement An electron in a finite square well has 6 distinct energy levels. If the finite square well is 10nm long determine: a) Approximate the possible values for the depth of the finite square well ##V_0##. b) Using a well depth value in the middle of the results obtained from part...

At the time of Big Bang the size of Universe equal the size of an atom.The Universe has expanded and the time from the Big Bang to the present is finite.Then at the present time the size of the Universe is finite or infinite?

Hi I've been trying to get a simple solution to the 2D Navier-Lame equations using finite difference on a rectangular grid. I want to see the displacements, u and v, when a simple deformation is imposed - e.g. top boundary is displaced by 10%. The equations are as follows: \begin{eqnarray*}...

Homework Statement Given an initial value problem: ##x'(t)=f(t,x)\,,x(t_0)=x_0## Use centered finite differences to approximate the derivative, and deduce a scheme that allows to solve the (ivp) problem. Homework Equations For centered finite differences ##\displaystyle\frac{dx}{dt} \approx...

Hi, I have a difficult time trying to perform the following integral, $$ j({T}, \Omega)=\int_0^{ T} d\tau \frac{\tau^2\exp(-i\Omega\tau)}{(\tau-i\epsilon)^2(\tau+i\epsilon)^2} $$ The problem is that the poles ##\pm i\epsilon## when taking the limit ##\epsilon\rightarrow 0## are located at...

Homework Statement I'm struggling to find a solution to exercise (*b). I have uploaded a pdf of the assignment. Please advise me at your convenience. Homework Equations x(x_l^+) = T(x_l^+, x_l^-)x(x_l^-) The Attempt at a Solution x(a^-) = \frac{\psi(a^-)}{\psi(a^-)} , T(a^+, a^-) \left(...

I just noticed in reading Griffiths that he places the base of the infinite square well at a zero potential while he places the base of the finite square well at a negative potential -V_0, where V_0 is a positive, real number; is there any reason for this? I just started learning about them/am...

Hello everyone, my question is about Euclidean correlators (say a 2-pt function to be specific) in presence of non-zero chemical potential. The question in particular is: is it still true that the Minkowski time ordered 2-pt function can be simply obtained from the Euclidean one by analytic...

A number of scientists subscribe to this theory. I read up on it, but none of the explanations I found really answered my questions. How should one attempt to envision a universe that is finite and bounded?

This question is in context of the recent gravitational wave detection by aLigo. Apparently aLigo has detected the entire process, including the before merger, during merger, and aftermath of the completed merger. My understanding is that two black holes should not be seen to be merging in...

Consider a finite series of repeated costs C that occur at a series of times ti. Is there a solution to discount these costs by interest rate r to account for time value of money, i.e. solve for S? The times ti of each cost are unknown, but the number of costs n is known, and the average time...

I am solving some 2nd order differential equations using the finite element method. Doing so I represent the second order derivative at a given point as: ∂2ψi/∂x2 = 1/(Δx)2 (ψi-1+ψi+1-2ψi) And solve the differential equation by setting up a matrix of N entries and solving for the eigenvectors...

Hello! (Wave) I want to show that a group with finite number of subgroups has to be finite. I thought to suppose that the group is not finite and then get a contradiction.So, suppose that the group is not finite. Then the group has infinite elements. Since the group has a finite number of...

Homework Statement Show that finite dimensional normed vector spaces are complete. Homework Equations ##E## is a finite dimensional vector space and ##N## a norm on ##E## The Attempt at a Solution If ##\{x_n\}_n## is a Cauchy sequence in ##(E,N)##, then it is bounded and each term of the...

what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure

Homework Statement A finite line of uniform charge is on the line joining (4,0,0) (0,8,0) and has λ= 2μC/m find E at (0,0,0) Homework Equations E = Q / (4 π ε0 r^2) dQ = λ dl = λ dx The Attempt at a Solution I first notice that r will depend on 2 changing values x and y. I write an...

If $G$ is a finite group, show that there exists a positive integer $N$ such that $a^N = e$ for all $a \in G$. All I understand is that G being finite means $G = \left\{g_1, g_2, g_3, \cdots, g_n\right\}$ for some positive integer $n.$

Please,I am working on the criticality calculation of an homogeneous finite cylindrical reactor core using four-group diffusion equations. I have been able to discretize the multigroup diffusion equations using the finite difference method(FED). But I am stocked on the iterative method to...

Homework Statement Say x is an infinitesimal number on the hyperreal line, is this expression finite, infinite or infinitesimal Homework Equations (sqrt(4+x)-2)/x The Attempt at a Solution [/B] My approach so far has been that sqrt(4+x) is (2+y) where y is another infinitesimal and y<x...

Let F=Z2 and let f(x) = X^3 +x+1 belong to F[x]. Suppose that a is a zero of f(x) in some extension of F. Using the field created above F(a) Show that a^2 and a^2+a are zeros of x^3+x+1?

Hello! (Wave) The finite sequence of integers $Y_1, \dots, Y_M$ takes both positive and negative values, where $M$ is a fixed positive integer. Could you help me to find a formulation using dynamic programming that solves the problem of finding integers $i_1, i_2$ with $1 \leq i_1 \leq i_2...

I would like to know how to implement internal hinges in a program I'm developing. A hinge is created by changing the stiffness matrix of the beam. The problem is when two interconnected beams have a hinge at the same location, so basically we have a hinged joint, in this scenario I will obtain...

Ok my question: what is the difference between the binding energies of these 2 types of atoms, conceptual wise, which one is greater? I am assuming based on the easy calculations of the potential energy of the finite size atom ( inside and outside) There is a difference between the potential...

I've seen various, wildly different, estimates of the size of the Universe. Do we have evidence demanding that the Universe is finite in size? If so, what are the clues that lead us to estimate that size beyond absolute speculation?

Homework Statement Laser light with a wavelength 633 nm is used to illuminate two slits separated by 0.125 mm. The width of each slit is 0.0150 mm. Assuming that only fringes between the first minima in the pattern are counted, how many bright fringes are visible? lambda = 633nm d = 0.125mm w=...

I have a particle in a spherical well with the conditions that V(r) = 0 is r < a, and V(r) = V0 if r ≥ a. In this problem we are only considering the l=0 in the radial equation. After solving this I found that in the region 0<r<a, u(r)=Bsin(kr) (k=√2mE/hbar), and in the other region...

Homework Statement A finite solenoid with "N" turns of wire, "L" length , "R" is the radius of the solenoid and passes through it a current "I". The objective is to calculate "L" of a finite solenoid. Not the basic formula ##L=\frac{\mu_0·N^2·S}{Length}## which is for a infinite solenoid. See...

I think I am in a misconception concerning laser beams: Even the best lasers have a small line width. The spectral line is gauss-shaped. therefore the wave in position-pace is also a gauss-shaped wave packet, that travels with a certain group velocity. But this gauss shaped wave packet has a...

Homework Statement Find a recursive relation on the number of partitions ##P_n## for a set ##S_n## of cardinal ##n##. ##P_0 = 1## is given. Homework EquationsThe Attempt at a Solution A partition of ##S_{n+1}## is given by the choice of a non-empty ##k##-block ##A_k## of ##S_{n+1}## and a...

Homework Statement Find \sum\limits_{k=0}^{n}k^2{n\choose k}(\frac{1}{3})^k(\frac{2}{3})^{n-k} Homework Equations -Binomial theorem The Attempt at a Solution I am using the binomial coefficient identity {n\choose k}=\frac{n}{k}{{n-1}\choose {k-1}}: \sum\limits_{k=0}^{n}k^2{n\choose...

I've often wondered about what happens when you try to add up the potential due to everything in the universe in a Newtonian way, especially in the context of the "Sum for Inertia" which seems to suggest a connection between Mach's Principle and GR in the context of rotation. Today I noticed an...

Hi, one thing always bothered me about the argument on the size of the Universe. If it started about 13.7 bn years ago then how could it possibly be infinite in extent? Once the time was finite its not possible to attain infinite extent - no matter how fast it expands. Also if there was...

problem statement, all variables and given/known data A finite sheet of charge, of density ρ=2x(x2+y2+4)^3/2, lies in the z=0 plane for 0≤x≤2m and 0≤y≤2m.Determine E at (0,0,2)m Ans:(18x10^9)(-16/3ax-4ay+8az) Homework Equations E=kQ/R2 The Attempt at a Solution dE=ρdA / R^2 aR...

So, according to physicsoftheuniverse.com, "In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become (sic) infinite and space-time curves infinitely, and where the laws of physics as we...

Light, amount other things, have no mass, and therefore is able to attain the highest speed possible in this universe. Yet for some reason this speed is not infinite, as would what intuition dictate, but has a finite value. Would it be fair to say that the fact light, something that "should" be...

A 2-dimensional creature living on the surface of a 3-dimensional sphere could conclude he lives in a finite, unbounded universe. Is it necessary for a 3-dimensional creature to assume there is a 4th spatial dimension in order to conclude the universe is finite and unbounded? I have seen a...