Questions tagged [eigenvalues]

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13
votes
3answers
858 views

An ODE system easily polluted with spurious eigenvalues

I tried solving the eigenvalue problem of a 1st-order ODE system (see the code below) with NDEigenvalue. (One option I found in it seems to be ...
5
votes
1answer
144 views

How to control DifferenceOrder in NDEigenvalue for an ODE?

I am trying to solve the eigenvalue problem of a 1st-order ODE system using NDEigenvalue. It should be finite difference method for ODE. And I want to tune the the ...
2
votes
1answer
125 views

Why the sign of eigenfunctions obtained from NDEigensystem are flipped

I am trying to verify my hand solution for a HW problem using Mathematica. I noticed that I get correct eigenvalues from Mathematica using DEigenvalues but when ...
0
votes
1answer
104 views

Hermitian Matrix giving non-real eigenvalues

I am using the following code to find the eigenvalues of a tightbinding matrix ...
1
vote
0answers
61 views

Eigenvalues of a matrix?

I have declared this matrix in my notebook ...
17
votes
0answers
469 views

Wrong eigenvalues from a sparse matrix

Bug introduced after 5.0, in or before 8.0 and persisting through 12.0. I notice in the following example that wrong smallest 2 eigenvalues are resulted if calculating from a sparse matrix. But it ...
4
votes
1answer
275 views

Finding the eigenvalues (diagonalizing) of a block-diagonal matrix

I have a large $2^N \times 2^N$ matrix. It is the exact Hamiltonian of a spin chain model which I have generated with code I wrote in Fortran. The code block diagonalizes the Hamiltonian into constant ...
0
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0answers
24 views

Eigenvalues function not working properly [duplicate]

I am trying to simply find the Eigenvalues of any matrix. I have set up M to be a 3 by 3 matrix filled with random values: ...
1
vote
0answers
106 views

Problems with DEigensystem

I have the following problem $\frac{c_p q_m}{A}\frac{\partial T(x,t)}{\partial t}+\rho c_p \frac{\partial T(x,t)}{\partial x}-\lambda \frac{\partial^2 T(x,t)}{\partial x^2}=0$ I want to find the ...
1
vote
0answers
78 views

Cannot access 3-D Schrödinger eigenfunctions from NDEigensystem

The following solves the first 3 eigenvalues of the following simple 3D-Schrödinger equation, but I do not know how to use the interpolating eigenfunctions, i.e., ...
0
votes
2answers
176 views
6
votes
1answer
124 views

NDEigenvalues complains not Hermitian with large dimension differential operator

The following snippet calculates eigenvalues and eigenfunctions of a null operator (just as an example): ...
0
votes
2answers
84 views

DSolve and eigenvalues?

I have solved a system of $N$ ($N$ is the order of system) ODE with DSolve and found $N$ solutions in the form ...
0
votes
1answer
35 views

Assigning eigenkets to particular eigenspace depending on eigenvalues of system inside a module

I am writing a module, in which the Observable and State is given, so I need to write a function/module QuantumMeasurement, that will return a state of the quantum system resulting from the ...
0
votes
0answers
57 views

Solving 4th order polynomial [duplicate]

I have this 4x4 matrix $$ \hbar\left( \begin{array}{cccc} n \omega _0+\frac{\omega _1}{2}+\frac{\omega _2}{2} & \sqrt{n+1} g_2 & \sqrt{n+1} g_1 & 0 \\ \sqrt{n+1} g_2 & (n+...
13
votes
6answers
731 views

Solving this challenging ODE

Consider the ODE: $$w^{(4)}(x) + (L-x)w''(x) - w'(x) = 0 $$ with some of the following boundary conditions: free: $w'' = 0$, $w'''=0$, clamped: $w = 0$, $w'=0$, pivot: $w = 0$, $w''=0$. Two such ...
0
votes
0answers
279 views

Linear Stability Analysis of dynamical system

I'm starting to use Mathematica for some linear stability analysis of a discrete non-linear dynamical system. I can't find an on-line tutorial for it, and I'm quite at a loss (in fact I can't even ...
3
votes
1answer
59 views

Getting the overlap of NDEigenfunctions of different problems

I am solving a number of Schrödinger eigenvalue problems for an array of different potentials, and I would like to calculate, in a quick, efficient and natural way, the overlap between the different ...
0
votes
0answers
68 views

Testing a (numerical) matrix for positivity

I’ve been testing certain randomly-generated $6 \times 6$ symmetric (and also Hermitian) matrices ($H)$ for positive definiteness, using the command ($n$, of course, being a count variable), ...
0
votes
0answers
39 views

Eigenvectors calculation doesn't match from two identical results

I have a $3\times 3$ matrix, depending on a single parameter. My job is to find the eigenvectors for the matrix. I tried two ways, shown below ...
4
votes
0answers
270 views

Spectral problem for differential vector operator (calculation of EM field in a cavity)

I know that mathematica has a DEigensystem and NDEigensystem which allow one to find eigenfunction and ...
3
votes
1answer
182 views

Can NDEigensystem use arbitrary precision arithmetic?

Consider the following computation of an eigenfunction of 1D Laplacian on the interval of $[0,\pi]$: ...
22
votes
1answer
1k views

Eigenvalues broken in 11.2?

Bug introduced in 11.1.0 and fixed in 11.3.0 The code ...
17
votes
8answers
1k views

Tracking Eigenvalues Through a Crossing

Suppose I have a matrix which depends on some parameter. I want to compute the eigenvalues as a function of this parameter, and then plot them. For example, I may have a matrix representing the ...
1
vote
1answer
209 views

NDEigensystem in a complicated case

Apologies for a boring question. I am trying to modify the standard Mathematica example for my needs. The only differences in my case are: A more complicated potential (double-well, grows rapidly). ...
6
votes
1answer
472 views

NDSolve eigenvalue problem of bound state

I am trying to solve this eigenvalue problem: \begin{align} \mu \Psi(r) & = -\frac{1}{2}\left ( \Psi^{\prime \prime}(r) + \frac{2}{r} \Psi' (r)\right ) -4\pi \Psi(r) \int _0^\infty dr' r'^2 \frac{...
3
votes
2answers
322 views

Why ODE's naive finite difference matrix works well for different boundary conditions

We know finite difference method (FDM) can replace $y''(x)$ as $\frac{1}{h^2}[y(x+h)+y(x-h)-2y(x)]$ or so. The naive way to write down the matrix of the differential operator is like the following, ...
0
votes
0answers
60 views

plotting functions containing branch cuts and crossings

For Functions That Do Not Have Unique Values, mathematical chooses a specific value; when plotting, say, the eigenvalue of a matrix that has such branch cuts, if the eigenvalues do not cross each ...
7
votes
5answers
527 views

Spectral problem for differential operator

I want to find numerically eigenvalue and eigenfunctions some nontrivial differential operator. But I can not find, how to do it in Mathematica. For the sake of simplicity let us discuss the trivial ...
0
votes
1answer
324 views

Change of basis from one linear mapping to another [closed]

I have this PDE which looks like this $\frac{d\vec{x}}{dt}= A\vec{x}+B\vec{x}$ Where $A$ and $B$ are both $n\times n$ matrices, and $\vec{x}$ is a state vector. Without making this too complicated ...
17
votes
7answers
1k views

How to check if a vector is an eigenvector of a matrix using mathematica?

Here is a vector $$\begin{pmatrix}i\\7i\\-2\end{pmatrix}$$ Here is a matrix $$\begin{pmatrix}2& i&0\\-i&1&1\\0 &1&0\end{pmatrix}$$ Is there a simple way to determine ...
0
votes
1answer
144 views

No eigenvectors coming for a very simple* matrix

I have a question regarding the same as Problem with Eigenvectors when given a matrix containing approximate numbers and symbols and Why won't Mathematica obtain eigenvectors for this symmetric ...
0
votes
0answers
150 views

finding eigenenergy/eigenvector pairs

This is perhaps more of a mathematics question rather than a Mathematica one, but I am looking for an easy Mathematica solution. I have a real square matrix consisting of four smaller blocks $H = \...
5
votes
0answers
77 views

Bug for Cubics -> True in Eigenvalues?

Let's consider the simple code ...
4
votes
2answers
458 views

Eigenvalues and eigenvectors of tensors

I have a linear equation where the unknown is a matrix: $$\sum_{pq} T_{ijpq}X_{pq} = \lambda X_{ij}$$ This is an eigenvalue problem for the tensor $T_{ijpq}$. Mathematica ...
0
votes
0answers
91 views

How to solve the eigenvalue problem that arises in stability of flows

I am an undergraduate student and I want to know how to solve this hydrodynamic stability problem. I tried but all my efforts have failed. Your suggestions will help me a lot. The equations are <...
0
votes
0answers
31 views

Eigenvaules of a symbolic matrix [duplicate]

If I try to find the eigenvalues in following way, mathematica gives something else other than algebraic expression, how to obtain algebraic expression ??? Please suggest something . ...
3
votes
1answer
363 views

Eigenvalue/eigenvector reordering and/or renormalisation?

I have two functions $f(x,y),g(x,y)$ and a matrix $M=\begin{pmatrix}\frac{\partial f}{\partial x} & \frac{\partial f}{\partial y}\\\frac{\partial g}{\partial x} & \frac{\partial g}{\partial y}...
2
votes
2answers
320 views

Eigenvalues and plot are very slow

I'mt trying to find eigenvalues (and plot them) but the evaluation takes way too long. I don't think it supposed to be a complicated computations. What am I doing wrong? ...
9
votes
1answer
599 views

Finding Eigenvalues for a boundary value problem

I have a 10x10 linearized BVP which I can write as $$\mathbf{y}'(x) = \mathbf{A}(\omega) \mathbf{y}(x)$$ subject to boundary conditions $$\mathbf{B} \cdot \mathbf{y} = \mathbf{0}, \quad x=0 \\ \mathbf{...
0
votes
0answers
148 views

Eigenfunctions to a Sturm-Liouville problem

I am trying to find the first 5 eigensolutions to a Sturm-Liouville problem; I have tried the code; ...
5
votes
1answer
486 views

How to use DEigensystem with periodic boundary conditions on the derivative?

Since I found I can use DEigensystem to obtain eigenvalues and eigefunctions for differential operators, I am using it to verify solution to some of my HW's. In ...
0
votes
0answers
140 views

Eigenvalues of a symbolic 28×28 Hessian matrix

I have a little problem trying to calculate the eigenvalues of big symbolic (depending on $a$) Hessian matrices (28×28, 32×32 ...). I think I've understand, by reading other posts, that Mathematica ...
2
votes
0answers
82 views

DEigenvalues with Robin B.C. sign problem

To find eigenvalues for $y''=\lambda y$ with robin boundary conditions on one end, and Dirichlet on the other end, I am getting correct value when robin B.C. on the right side, but when I flip things, ...
0
votes
1answer
132 views

why is there a minus sign on DEigenvalues “operator” as compared to the ODE itself?

In Mathematica, to find the eigenvalues for the following differential equation \begin{align*} y''(x)+ \lambda y(x) &=0 \\ y(0) &=0\\ y(L) &=0 \end{align*} The syntax one ...
5
votes
1answer
277 views

How to specify both DirichletCondition and NeumannValue on DEigenvalues?

Ok, I give up :) I am trying to verify the eigenvalues for heat PDE in 1D, when left end has homogeneous DirichletCondition but the right end is insulated, so it ...
2
votes
2answers
363 views

Problem with NDEigensystem

Consider the Sturm-Liouville problem $$y''(x) + \lambda x^2 y=0, \ y(0)=0,\ y(1)=0$$ The analytical solution is given by $$\lambda_n=4\alpha_n^2, \ y_n(x)=\sqrt{x}J_\frac14(\alpha_nx^2)$$ ...
3
votes
2answers
314 views

Using NDEigensystem to solve coupled eigenvalue problem

I want to find the Eigenvalues and Eigenfunctions for the following Eigenvalue problem I tried to solve this numerically ...
0
votes
1answer
143 views

How to solve the following system with NDSolve and FindRoot? Please address

Consider the following coupled systems of equations $f′′− k^2 f=k\, \mathbf{Ra}$ and $g′′− k^2 g=k\,f$ , where $f$ and $g$ are functions of $z$. The boundary conditions for the problem are $f=0$ and ...
5
votes
2answers
195 views

Checking if a symbolic symmetrical Matrix is negative definite

I have the following problem finding the value ranges for the parameters of a symbolic symmetrical matrix in order to make it negative definite: The matrix I'm talking about looks as follows ...