Finite Definition and 1000 Threads

Homework Statement ψx is the function of postion for a particle inside a 1D finite square well. Write down the expression for finding the particle a≤x≤b. Do not assume that ψx is normalised. Homework Equations The Attempt at a Solution This is to check I'm not going insane: P...

Homework Statement The problem statement is attached. The Attempt at a Solution I know how to solve the problem. However, my teachers solutions notes and my book's do it differently, and I want to ask what the difference is, so I have attached them both. My book does it the way I did it. My...

show that H is subgroup of finite index in Z^n exactly when H is free comutative group of rank n

Homework Statement Prove: If ##X## is a (possibly infinite dimensional) locally convex space, ##L \leq X##, ##dimL < \infty ##, and ##M \leq X ## then ##L + M## is closed. Homework Equations The Attempt at a Solution ##dimL < \infty \implies L## is closed in ##X## ##L+M = \{ x+y : x\in L, y...

There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point...

Homework Statement A ball is dropped from a 100 feet and has a 90% bounce recovery. How many bounces does it take for the ball to travel 1854.94320091 feet? Homework Equations -None- The Attempt at a Solution I know the ratio is .9 and the 'a one' value is 180, so I plugged those values in...

Homework Statement Let H be an \infty-dimensional Hilbert space and T:H\to{H} be an operator. Show that if T is compact, bounded and has closed range, then T has finite rank. Do not use the open-mapping theorem. Let B(H) denote the space of all bounded operators mapping H\to{H}, K(H) denote...

Hello to everyone, while solving homework course Nanotechnology and Nanocomponents, I have encountered a problem in FD method that is applied in even potential. In my homework assignment it is explicitly said that it must be done only in x>0 part of the domain, where my problem starts with...

Homework Statement If an electron is in a finite quantum well and it's E>V{0} what does the wave function look like? Homework Equations The Attempt at a Solution Wondering if anyone could help me out with this? I know that outside the well the electron will have the same...

Structural Analysis-Writing Finite Element Code, Dear all, I have written a code ( in fact it is a software) for 3D finite element structural analysis. While developing the code I found that assembling global stiffness matrix is quite complicated. The complication is even more when we...

Hey guys! New guy here so bear with me on my first post:) I'm trying to calculate the B field in the center of a finite solenoid for different outer radius sizes. I was able to find a formula online that gave the B field in the center of a solenoid given its length, inner radius, outer...

Homework Statement If $$f(x)>0$$ is continuous for all $$x\ge0$$ and the improper integral $$\int_0^{\infty}f(x) dx$$ exists, then $$\lim_{x\rightarrow\infty}f(x)=0.$$ 2. Relevant I think this assertion is false. A counterexample can be constructed along the following lines of...

I'm reading the following article by Maxwell Rosenlicht: http://www.jstor.org/stable/2318066 (The question should be clear without the article, but I present it here for reference.) In the beginning of the article he discusses differential fields (i.e. a field F with a map F\to F...

How to evaluate the following expression? \sum_{i=0}^{N} \binom{N}{i} \left(-1\right)^{i}\left(\frac{1}{2+i}\right)^{k} regards, Bincy

I tried to find the potential of a finite line of charge with length 2l and constant charge density \lambda .So I set up the coordinates somehow that the line is on the x-axis and the origin is at the center of the line.Then I did the following: \phi=\int_{-l}^l \frac{\lambda dx'}{4 \pi...

Does the universe has boundaries?, is it finite?

For any set S, the natural numbers N and function f, if f : S → N is injective but not surjective, is S finite?

Homework Statement Let p be an odd prime. Then Char(Z_p) is nonzero. Prove: Not every element of Z_p is the square of some element in Z_p.Homework Equations The Attempt at a Solution I first did this, but i was informed by a peer that it was incorrect because I was treating the congruency as...

T ≡ "two coins tossed 7 times by two people A and B giving outcomes [A^+B^+, A^-B^+, A^+B^-, A^-B^+, A^+B^+, A^-B^-, A^-B^+], where + = heads and - = tails" Calculate P(A^+B^+|T), P(A^+|T), P(B^+|T) and P(B^+|T,A^+) I asked this question elsewhere and there was a suggestion that the question...

hey guys i have a question. i solved the problem but i don't understand how to do it. Two perpendicular straight wires join in the ends of a semicircular loop of radius a = 11 cm, as shown in the figure above. If the current I =6 A, what is the resultant field at the center of the circular...

Homework Statement Solve Explicitly the first two eigenfunctions ψ(x) for the finite square wave potential V=V0 for x<a/2 or x>a/2, and V=0 for -a/2<x<a/2, with 0<E<V0. Homework Equations See image The Attempt at a Solution See image. After modeling an in class example, my classmates and i...

Hello, I have a question about Schrodinger's equation and the finite well. It isn't so much as a math question but rather how to interpret the problem. I'll use the picture on the right from here for reference and for simplicity, I'll stick to one dimension. When I think of this problem, I...

I want to come up with examples that finite complement topology of the reals R is not Hausdorff, because by definition, for each pair x1, x2 in R, x1 and x2 have some disjoint neighborhoods. My thinking is as follows: finite complement topology of the reals R is a set that contains open sets...

I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6 (see attachment - pages 5 -6 Grove and Benson) we find the following statement: "It is easy to verify (Exercise 2.1) that the vector x_1 = (cos \ \theta /2, sin \ \theta /2 )...

Dear all, I have written a code for dynamic analysis of a mechanical structure. My primary purpose is to find natural frequencies of the structure. When I test my code for a cantilever bar whose natural frequencies are known analytically, I found a big difference between the the first...

Homework Statement Hi! I have a question about calculating electric field made by finite point charges q_{1},q_{2},..., q_{n}. From the book "introduction to electrodynamics", you can see that the electric field E at a point P made by the finite point charges can be calculated by the below...

Hi, can someone please help me with this problem. Let A be an open subset of the interval [0; 1]. 1. Show that the set W = {C(x) : x is in A} is countable or finite. This is what I have... Suppose W is an infinite subset of N. Then we have f : W-> N, which is one-to-one. By the fact that...

How do I prove that a Hausdorff topological space E is finite dimensional iff it admits a precompact neighborhood of zero?

\int^{\infty}_{1}\frac{1}{e^{t}-1}dt = -ln(e - 1) + 1 Not sure how to get the +1 part from infinity, seems like it should be infinity, i.e. ln(e^{\infty} -1) = ? Any help appreciated, thanks.

Dear all, I have written a code for structural analysis using the finite element method. For some reason, I directly started with 3D elements ( hexahedron). I used to believe that the code was fine but recently i realized that the results ( deformation, natural frequency,..) strongly depend...

Homework Statement Check the title Homework Equations Using the following definition of finite/infinite: A set X is infinite iff \exists f:X \rightarrow X that is injective but f(X) \not= X, i.e. f(X) \subset X. A set X is finite iff \forall f:X \stackrel{1-1}{\rightarrow} X it must follow...

Hi all, A fixed-free bar has a single natural frequency. When we discretize such a bar in the finite element method, then the natural frequencies are the eigenvalues and an nχn matrix where n is the number of the degree of freedom which is usually large. Thus we obtain up to n natural...

If the universe is finite then what is beyond? If infinite then how can humanity conceive the 'big picture'?

Homework Statement Prove that the analytic function e^z is not a polynomial (of finite degree) in the complex variable z. The Attempt at a Solution The gist of what I have so far is suppose it was a finite polynomial then by the fundamental theorem of algebra it must have at least...

Hi, dear all, recently study the solid mechanic continuity, keep reading about to solve large deformation of material, you will need so called "finite elasticity" What is this finite elasticity refer to ? "Finite elasticity is a theory of elastic materials capable of undergoing large...

Homework Statement Homework Equations The Attempt at a Solution

Hi all, I need to do a dynamic structural analysis using finite element method and I have a question about the mass matrix. Question: I have the force per nodes and I need to calculate the displacement of each node at a given time. For this purpose, it seems that I need to distribute the...

Homework Statement We are given the ring Z/1026Z with the ordinary addition and multiplication operations. We define G as the group of units of Z/1026Z. We are to show that g^{18}=1. Homework Equations The Euler-phi (totient) function, here denoted \varphi(n) The Attempt at a Solution...

Homework Statement Show the following sets are countable; i) A finite union of countable sets. ii) A countable union of countable sets. Homework Equations A set X, is countable if there exists a bijection f: X → Z The Attempt at a Solution Part i) Well I suppose you could start by considering...

So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding. Firstly, how do...

I have been banned, maybe my nickname was not so kind. I let the topic continue here. I report my last comment: "Ok, I got the point. thanks for replying! It's just a change of basis that under boundary condition diagonalize the Hamiltonian. But then a subtle point: In order for...

Hi all, I have a question. For sure the momentum representation used in solid state physics works for infinite lattices or periodic ones. But when it comes to finite lattice, i.e. 100 sites, can the momentum representation be used? What are the errors? Where does this fail? Thanks for...

I am reading Dummit and Foote on Representation Theory CH 18 I am struggling with the following text on page 843 - see attachment and need some help. The text I am referring to reads as follows - see attachment page 843 for details \phi ( g ) ( \alpha v + \beta w ) = g \cdot ( \alpha v +...

Assume that you have a one dimension box with infinite energy outside, and zero energy from 0 to L. Then my understanding of the Schrodinger equation is that the equation inside will be: -h^2/2m*d2/dx2ψ = ihd/dtψ And the energy eigenstates are given by ψ(x,t) = e-iwt*sin(kx) where k = n*π/L...

Homework Statement to prove that a function bounded on [a,b] with finite discontinuities is Riemann integrable on [a,b] Homework Equations if f is R-integrable on [a,b], then \forall \epsilon > 0 \exists a partition P of [a,b] such that U(P,f)-L(P,f)<\epsilon The Attempt at a...

How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?

I have seen descriptions for an algorithm that can take a regular deterministic finite automata and create a non-deterministic finite automata that is guaranteed to generate the reverse of string accepted by the DFA. Does anyone know of a "formal" proof that shows this is true in all cases...

Homework Statement Let S be a linearly independent subset of a Hilbert space. Prove that span(S) is a subspace, that is a linear manifold and a closed set, if and only if S is finite. Homework Equations The Attempt at a Solution Assuming S is finite means that S is a closed set...

Linear Algebra Preliminaries in "Finite Reflection Groups In the Preliminaries to Grove and Benson "Finite Reflection Groups' On page 1 (see attachment) we find the following: "If \{ x_1 , x_2, ... x_n \} is a basis for V, let V_i be the subspace spanned by \{ x_1, ... , x_{i-1} ...

I am reading Grove and Benson's book on Finite Reflection Groups and am struggling with some of the basic linear algebra. Some terminology from Grove and Benson: V is a real Euclidean vector space A transformation of V is understood to be a linear transformation The group...