Eigenvalue problem Definition and 85 Threads

A is a simetric metrices nxn. so v\in R^n and v\neq 0 so (\lambda I -A)^2=0 for some \lambda prove that for the same v (\lambda I -A)=0 how i tried to solve it: i just collected data from the given. simetric matrices is diagonizable. B=(\lambda I -A) we were given that B^2v=0 so...

Hello everyone, I am solving an eigenvalue problem. Right now, I would like to know; How to determine the degeneracy of eigensolution of sturm-liouville differential eigenvalue problem? I have an eigenvalue sturm-liouville problem H f(y) = E f(y) where H is a differential operator and E is...

Homework Statement Solve the differential equation eigenvalue problem: f'' + \lambda f = 0, \quad 0 \leq x \leq 4\pi, \quad \text{where} \quad f^{'}(0) =0, \quad f^{'}(4\pi) = 0, \quad \text{and} f \neq 0. Consider ONLY \quad \lambda \geq 0, \quad and find the values of \quad \lambda...

I have a PDE test next week and I'm kinda confused. How do you prove that eigenvalues are all positive? I know Rayleigh Quotient shows the eigenvalues are greater than or equal to zero, but can someone explain the next step. Thanks in advance

Hi, this is probably really basic for anyone really good with MAPLE but I just solved an Eigenvalue problem in MAPLE and it displays the answer for lambda as a list since my problem contained a 6x6 matrix. My problem is that I want to be able to perform an operation of each individual output...

Homework Statement I am having some trouble with this procedure and I am not exactly sure how to phrase my questions; so I will procede with one particular problem that is giving me trouble and perhaps someone can help to shed light on it. :smile: In one problem, I am given some matrix...

Homework Statement Given that q is an eigenvalue of a square matrix A with corresponding eigenvector x, show that qk is an eigenvalue of Ak and x is a corresponding eigenvector. Homework Equations N/A The Attempt at a Solution I really haven't been able to get far, but; If x is an...

Given the Euler equations in two dimensions in a moving reference frame: \frac{\partial U}{\partial t} + \frac{\partial F\left(U\right)}{\partial x} = 0 U = \left(\rho , \rho u , \rho v , \rho e \right) F\left(U\right) = \left(\left(1-h\right)\rho u , \left(1-h\right)\rho u^2...

"solution to an eigenvalue problem" ? I am trying to reproduce the results from a paper. The essence of the paper is hidden in just one equation (eq. 11) and some lines of text. For me this is going somewhat too fast. Below are the essential parts of the paper, describing the problem (and...

Homework Statement There is an Hamiltonian operation which is given by (2 1 1) (1 2 1) = H ; 3-by-3 matrix (1 1 2) And let's have an arbtrary eigenvector (a) (b) = v ; (3x1) matrix (c) Then, from the characteristic equation, the eigenvalues are 1,4. Here eigenvalue 1 is...

Hi. I was wondering if anyone can give me advice on how to answer the following question. Use Gerschgorin's theorem to show the effect of increasing the size of the matrix in your solution to the eigenvalue problem: y''+lambda*y=0 y(0)=y(1)=0 Thanks Main issue is that I don't...

[URGENT] another Eigenvalue problem Homework Statement [PLAIN]http://img99.imageshack.us/img99/1762/222n.png Homework Equations N/A The Attempt at a Solution I've no clue what's going on for this one. What does that function even do anyway?

[URGENT] Eigenvalue problem Homework Statement [PLAIN]http://img228.imageshack.us/img228/4990/111em.png Homework Equations Sturm-Liouville equation? The Attempt at a Solution I guess I'm just totally lost here. I've no idea how to start. It seems to me that maybe solving for...

Homework Statement [PLAIN]http://img28.imageshack.us/img28/5227/79425145.jpg The Attempt at a Solution I'm not exactly sure how to go about this problem. How do I start?

Suppose P: V->V s.t. P^2 = P and V = kerP + ImP (actually not just + but a direct sum). Find all eigenvalues of P. ---- Which of the following explanations is right? (1 is an eigenvalue, but is 0 also?) Could somebody please explain? ----- First answer: Suppose that λ is an...

I'm trying to teach myself quantum mechanics using a book I got. I made an attempt at one of the questions but there are no solutions or worked examples so I'm wondering if I got it right. Here it goes Homework Statement Suppose an observable quantity corresponds to the operator \hat{B}=...

Homework Statement Let A be an nxn matrix and let I be the nxn identity matrix. Compare the eigenvectors and eigenvalues of A with those of A+rI for a scalar r. Homework Equations The Attempt at a Solution I think I should be doing something like this: det(A-\lambdaI), and...

Hi, Is there any solution for the following problem: Ax = \lambda x + b Here x seems to be an eigenvector of A but with an extra translation vector b. I cannot say whether b is parallel to x (b = cx). Thank you in advance for your help... Birkan

Homework Statement I would like to know what the definition of a Differential Eigenvalue Problem is please? I am a maths undergraduate. Homework Equations \lambda y = L y, where \lambda is eigenvalue, L is a linear operator. The Attempt at a Solution I have searched via google...

Homework Statement In Uniform Acceleration Motion, the force F is constant. then potential V(x)=Fx, and Hamiltonian H=(p^2/2m)-Fx The problem is to solve the eigenvalue problem Hpsi(x)=Epsi(x) Homework Equations F=constant V(x)=Fx H=(p^2/2m)-Fx The Attempt at a Solution I have...

Homework Statement Bessels equation of order n is given as the following: y'' + \frac{1}{x}y' + (1 - \frac{n^2}{x^2})y = 0 In a previous question I proved that Bessels equation of order n=0 has the following property: J_0'(x) = -J_1(x) Where J(x) are Bessel functions of...

Homework Statement solve the eigenvalue problem ∫(-∞)x dx' (ψ(x' ) x' )=λψ(x) what values of the eigenvalue λ lead to square-integrable eigenfunctions? The Attempt at a Solution ∫(-∞)xdx' (ψ(x' ) x' )=λψ(x) differentiate both sides to get ψ(x)x=λ d/dx ψ(x) ψ(x)x/λ=...

Solve the eigenvalue problem \frac{d^2 \phi}{dx^2} = -\lambda \phi subject to \phi(0) = \phi(2\pi) and \frac{d \phi}{dx} (0) = \frac{d \phi}{dx} (2 \pi). I had the solution already, but am looking for a much simpler way, if any. EDIT: Sorry that I accidentally posted...

Why did Schrodinger call his equation eigenvalue problem? We can solve Schrodinger equation since it's just differential equation with complex number

Find a 2\times 2 matrix A for which E_4 = span [1,-1] and E_2 = span [-5, 6] where E_(lambda) is the eigenspace associated with the eigenvalue (lambda) relevant equations: Av=(lambda)v The Attempt at a Solution I've pretty much gotten most of the eigenspace/value problems down, but this...

Homework Statement operator is d2/dx2 - bx2 function is psi=e^-ax2 if this fuction is eigenfuction for this operator, what is "a" and "b" constants value? Homework Equations The Attempt at a Solution

Homework Statement Consider the following problem: if \ A \psi=\lambda\psi,prove that \ e ^ A \psi=\ e ^\lambda\psi Homework Equations The Attempt at a Solution This is my attempt.Please check if I am correct. If \ e ^ A \psi=\ e ^\lambda\psi is correct, we should...

Solve the eigenvalue problem O_{6} \Psi(x) = \lambda \Psi(x) O_{6}\Psi(x) = \int from negative infinity to x of dxprime *\Psi(xprime) * xprime what values of eigenvalue \lambda lead to square integral eigenfuctions? (Hint: Differentiate both sides of the equation with respect to x) Im...

Hi, This is just a quick question -- I'm puzzled by the way this answer sheet represents the potential function. The question asks us to determine the energy eigenvalues of the bound states of a well where the potential drops abruptly from zero to a depth Vo at x=0, and then increases...

Homework Statement Find the eigenfunctions and eigenvalues for the operator: a = x + \frac{d}{dx} 2. The attempt at a solution a = x + \frac{d}{dx} a\Psi = \lambda\Psi x\Psi + \frac{d\Psi}{dx} = \lambda\Psi x + \frac{1}{\Psi} \frac{d\Psi}{dx} = \lambda x + \frac{d}{dx}...

Homework Statement Two square matrices A and B of the same size do not commute.Prove that AB and BA has the same set of eigenvalues. I did in the following way:Please check if I am correct. Consider: det(AB-yI)*det(A) where y represents eigenvalues and I represents unit matrix...

This is for a spin 1 particle. I can't get the determinant to come out right. Can someone show me what i am doing wrong

I'm stuck on the following eigenvalue problem: u^{iv} + \lambda u = 0, 0 < x < \pi with the boundary conditions u = u'' = 0 at x = 0 and pi. ("iv" means fourth derivative) I look at the characteristic polynomial for lambda > 0 and < 0 and I get fourth roots for each of them. In the case...

I have this eigenvalue problem: \frac{\mbox{d}^2y}{\mbox{d}x^2}+\left(1-\lambda\right)\frac{\mbox{d}y}{\mbox{d}x}-\lambda y = 0 \ , \ x\in[0,1], \ \lambda\in\mathbb{R} y(0)=0 \frac{\mbox{d}y}{\mbox{d}x}(1)=0 Then, I have to show that there exists only one eigenvalue \lambda , and...

I am having trouble with the following question. (Just hoping to get some guidance, recommended texts etc.): "Consider an eigenvalue problem Ax = &lambda;x, where A is a real symmetric n*n matrix, the transpose of the matrix coincides with the matrix, (A)^T = A. Find all the eigenvalues and...