Eigenvalue Definition and 382 Threads

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}...

Shankar 163 Homework Statement Show that for any normalized |psi>, <psi|H|psi> is greater than or equal to E_0, where E_0 is the lowest energy eigenvalue. (Hint: Expand |psi> in the eigenbasis of H.) Homework Equations The Attempt at a Solution I think the question assumes...

I need a bit of explanation on the conditions under which there is an eigenvalue that is equal to zero and what it's "physical" meaning. Thanks in advance.

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...

Dear experts! I have a small Hermitian matrix (7*7 or smaller). I need to find all eigenvalues and eigenvectors of this matrix. The program memory is bounded. What method is optimal in this case? Can you give any e-links? Thanks In Advance.

eigenvalue "show that" Homework Statement Let A be a matrix whose columns all add up to a fixed constant \delta. Show that \delta is an eigenvalue of AHomework Equations The Attempt at a Solution My solution manual's hint is: If the columns of A each add up to a fixed constant \delta, then...

Find the Eigenvalues of the matrix and a corresponding eigenvalue. Check that the eigenvectors associated with the distinct eigenvalues are orthogonal. Find an orthogonal matrix that diagonalizes the matrix. (1)\left(\begin{array}{cc}4&-2\\-2&1\end{array}\right) I found my eigenvalues to...

Hi All! Preliminaries: Let H denote the Hilbert-space, and let A be a densely defined closed operator on it, with domain $D(A) \subset H$. On D(A) one defines a finer topology than that of H such way that f_n->f in the topology on D(A) iff both f_n->f and Af_n->Af in the H-topology. Let...

Hi Guys, I have got some enquires for eigenvalue and eigenvector. Consider the 1st matrix: A = [ 1 2 3] [ 0 5 6] [ 0 6 5] The characteristic polynomial is det(A-λI) = [ 1-λ 2 3] [ 0 5-λ 6] [ 0 6...

I have two questions 1. If I have a 2x2 matrix A with entries a, b, c, d where a is the upper left corner, b upper right corner, c lower left, and d lower right. I have eigenvalues L1 and L2. I need to show that L1^2 + L2^2 <= a^2 + b^2 + c^2 + d^2. So far I've done this: I know...

Hi, I have troubles solving this question: Given the general DC motor governed equation, find the control voltage such that the speed w tends to constand reference input w* and the convergence rate is determined by the desired eigenvalues L1 and L2. I think it's easy to find the control...

Hello all, I'm stuck on this question, and I would appericate if someone can tell me how to start cracking the problem. I have a infinite square well, and is given a wavefunction that exist inside the well. The problem is to find the probability that a measurement of the energy will...

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Hi Given a 3x3 matrix A = \[ \left[ \begin{array}{ccc} 0 & 0 & 1+2i \\ 0 & 5 & 0 \\ 1-2i & 0 & 4 \end{array} \right] I need to a another 3x3 which satisfacies D = U^-1 A U Step 1. Finding the eigenvalues 0 = det(A- \lambda I ) = (0- \lambda)(\lambda - 5) (\lambda -4...

Hello, all, This is my fisrt time post on this forum, I have this question for long time but people around me couldn't really answer it, hopes I can get the answer from you guys... Given a complex n by n matrix A, Under what restriction, its eigenvalue(s) is the continuous function of A?

Given:Second order ODE: x" + 2x' + 3x = 0 Find: a) Write equation as first order ODE b) Apply eigenvalue method to find general soln Solution: Part a, is easy a) y' = -2y - 3x now, how do I do part b? Do I solve it as a [1x2] matrix?

Find a general solution of the given system using the method (A - \lambdaI)V2 = V1. x'_1 = 2x_1 - 5x_2, x'_2 = 4x_1 - 2x_2 x' = \left(\begin{array}{cc}2&-5\\4&-2\end{array}\right) characteristic equation: (2 - \lambda)((-2) - \lambda) + 20 = 0 \lambda^2 + 16 = 0 \lambda = 4i Using this...

Why has the x-axis have an eigenvalue = 1 and the y-axis an eigenvalue =-1? (please stay simple in your answers)

Hi guys, I've been given this question as part of my homework assessment however i don't even know what its asking me to solve :( I am sure you have to apply it to a certain equation but it doesn't say what! The question is: "Write down the eigenvalue equation for the total energy operator...

why is (psi)n=Asin(npix/L) the energy eigenvalue?

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 am studying Sturm-Liouville eigenvalue problems and their eigenfunctions form a "complete set". Can someone explain to me what this means?

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...

what is an eigenequation? what is the purpose of the eigenvalue? how does this fit into the schrodinger equation (particle in a box problem) ?

How do you prove that det(A) = \lambda_1*\lambda_2*...*\lambda_n, where \lambda_i is the eigenvalues of A? I'm stuck :cry:

I'm having trouble finding the eigenvalue for a given graph; but more specifically I can't seem to find the characteristic polynomial. My book tells me that the characteristic polynomial of a simple graph with n vertices is the determinant of the matrix (A-\lambdaI), where A is the adjaceny...

hi, if an operator O has the property that O^{4}f(x)=f(x), what are the eigenvalues of O? any hints on how to go about this?

Suppose there is a matrix A such that A-1 = A. What can we say about the eigenvalue of A, g? 1) Ax = gx 2) A-1 Ax = A-1 gx 3) Ix = g A-1x 4) x = g Ax 5) x = g gx 6) 1x = g2x Therefore 7) g2 = 1 8) g = 1 or g = -1 But suppose A = I (the identity matrix). For I, the only...

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...

can anyone explain the the real meaning and purpose of eigen vlaue and eigen vectors.. :smile:

I was recently asked to explain the eigenvalue condition, but I'm sure exactly which condition the inquirer was asking about. Are any of you nerds familiar with the Eigenvalue Condition? If so, please enlighten me. eNtRopY