Questions tagged [eigenvalues]
Questions on symbolically or numerically determining the eigenvalues of matrices (Eigenvalues, Eigensystem) or differential equations (DEigenvalues, DEigensystem, NDEigenvalues, NDEigensystem) in Mathematica. Also includes determining the eigenvalues of differential equations with DSolve or NDSolve.
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Possible bug in Eigensystem [closed]
I'm getting some very strange behavior when running Eigensystem on a 8000 by 8000 matrix of Real numbers (stored as a dense matrix ...
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2
votes
1
answer
133
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Numerical ground state wavefunction of Schrödinger equation with a Coulomb potential in 2D from NDEigensystem
I want to numerically solve the ground state wave function of the hydrogen atom with the Coulomb potential using the NDEigensystem. Here is the code to get the ground state wave function from the ...
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Problem to solve computationaly and plot the phase portrait of a nonlinear ode system
I am here again to see if some one can help me.
This time, I have problem to solve, computationally and plot the phase portrait of a nonlinear ode system (The Duffing Equation with just the spring ...
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votes
1
answer
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Eigenvalue Problem - Nullspace Basis
I need to solve an eigenvalue problem where some of the eigenvalues are 0. Due to the fact that I just need the eigenvectors associated to the 0-eigenvalues in some cases I'd just like to calculate ...
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Using Mathematica to find the eigenvectors
I would like some clarification about solving for eigenvectors in Mathematica.
I am looking at the following matrix:
\begin{equation*}
L =
\begin{pmatrix}
0 & m(1+\frac{kmwr}{\lambda}) \\
q(1-kpx)...
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0
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37
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Root function in the output [duplicate]
I was calculating the eigenvalues of a matrix and the output contained some eigenvalues like:
...
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1
answer
49
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Minimum eigenvalues of a matrix with two parameters
I have a $12 \times 12$ matrix $K$ depending on 2 parameters, $k$ and $\beta$ ($k=0.1,0.2,0.3,0.4$ and $\beta=0.1,0.2,0.3$). The analytical expressions of its eigenvalues are too cumbersome to ...
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3
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How do I get a coefficient matrix from a second order ODE's system?
I got this system:
I need to transform this ODE system in a matrix form, because I need to evaluate its stability and, further, plot the eigensystem with the Stream Plot function.
Is there any ...
3
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1
answer
57
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Discrepancy between `IGEigenvectorCentrality` and `EigenvectorCentrality` in Mathematica
I've been experimenting with directed graphs in Mathematica and I'm having some difficulty understanding the differences between IGEigenvectorCentrality and ...
- 155
2
votes
1
answer
210
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Solving Schrödinger equation for Dirac comb potential (kicked rotor)
I need to solve the Schrödinger equation for a Dirac delta potential. I could not find the correct way to write the time-dependent potential and how to solve the time-dependent equation for it.
The ...
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3
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2
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Eigenvalues and classification of critical points [closed]
I started with a function (x,y) and tried to write the code to work out the eigenvalues and classify the critical points.
The output it all good up until I try to use Which[] to classify the critical ...
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How can we get a compact form of the Eigenvalues?
I want to get a compact form of the eigenvalues of this matrix
Eigenvalues[({
{-r, p1, 0, 0},
{p1, -r, 1, 0},
{0, 1, r, p2},
{0, 0, p2, r}
})]
...
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3
votes
2
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146
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Plotting regions with zero eigenvalues of a matrix
I have a series of matrices exemplify as
\begin{align}
Atmp=\left(
\begin{array}{cccccccc}
0. & 0. & 1.\, +0.5 e^{-i z} & 0. & 1. y+0.2 & 0.\, +0.75 i & 0. & 0. \\
0. &...
- 801
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Manipulate incorrectly evaluating eigenvalues
I'm working with a system of differential equations. In this system there are 7 coefficients that I want to simulate numerically to find the eigenvalues at possible coefficients values.
First I ...
- 143
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1
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131
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Why do the eigenvalues periodically change with successive increase in the consideration region?
When finding the eigenvalues and eigenfunctions of the system Hc[r, z] using NDEigensystem, the following issue arises: When ...
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2
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Computing the continuous eigenvalues of a family of matrices
I want to compute the eigenvalues of a family of $2 \times 2$ unitary matrices $M: [0, 2 \pi] \to U(2), k \mapsto M(k)$, which is given by
\begin{align*}
M(k) = \frac{1}{2} \, \begin{pmatrix}
...
- 103
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Wrong eigenvalues for 2D QHO using DEigensystem[]
I try to solve 2D Quantum Harmonic Oscillator using DEigensystem[] in Mathematica 13.0. Here is my code:
...
- 11
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0
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35
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Unable to plot quasinormal modes using the QNMspectral package
I am trying to follow the advice provided in this paper by Aron Jansen to calculate the Quasinormal modes of a Dyonic AdS black hole (see Sec 4. of the paper) for which I use his package QNMspectral. ...
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1
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1
answer
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Issue with numerical evaluation of eigensystem
I am calculating eigenvalues of a Hamiltonian numerically but I am getting avoided crossings and gap in the curves (see the output of the code) which are not correct. Please help me out to resolve ...
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88
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How should a function written through the Module be written in the FindMinimum correctly?
There is a function that is written using a module ...
- 1,753
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1
answer
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What is the correct way to use FindMinimum with NDEigensystem?
I would like to find the minimum of a function dE[me_, mh_, e0_] using FindMinimum but Mathematica shows errors from ...
- 1,753
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1
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73
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Eigenvalue function finds real eigenvalues for antihermitian matrix
If given a (large) antihermitian matrix, Mathematica occasionally finds real eigenvalues although the in-build function AntihermitianMatrixQ confirms it to be antihermitian. The matrices for which I ...
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1
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Why does NDEigensystem not show the minimum eigenvalue for a certain parameter range in the cylindrical coordinate system?
In my previous question Why NDEigensystem does not show the minimum eigenvalue?, I asked why the NDEigensystem does not show the minimum eigenvalue for the ...
- 1,753
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1
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109
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calculate the eigenvalue of a complex hamiltonian (graphene)
I have a doubt about the calculation of the eigenvalue of the graphene Hamiltonian.
$ H = \begin{pmatrix}
0 & \Delta & \\
\Delta^{*} & 0& \\
\end{pmatrix}$
where $\Delta = \exp (-i a ...
- 599
1
vote
1
answer
105
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How to sort eigenvalues (from minimum to maximum) and their corresponding eigenvectors?
When using NDEigensystem, the first eigenvalue corresponds to the first eigenvector, the second eigenvalue to the second eigenvectors, and so on. I would like to sort the eigenvalues from min to max, ...
- 1,753
4
votes
2
answers
192
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Finding the sum of eigenvalues of a matrix depending on the parameters
There is a system that has the following Hamiltonian: $H=-\frac{1}{2}\Delta-\frac{1}{r}+\frac{B^2}{8}\rho^2-\frac{B}{2} (m + 2 m_s)$, where $r=(\rho,z,\phi), B=5, m=0, m_s=-1/2$. To find the ...
- 1,753
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3
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279
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Solid Mechanics FEM Simulation with Different Material Properties
How would I assign different material properties to the "bar" and "support"? Meaning, for example, the bar would be assigned the properties of single-crystal Copper and the support ...
- 7,485
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vote
1
answer
144
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Displaying NDEigensystem Results
I want to display a collection of deformed meshes in a GraphicsGrid where the surface colors are proportional to the displacement.
...
- 7,485
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64
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How can i know the number of times that an eigenvalue is degenerate for a large matrix?
As the title says I have a large sparse matrix, 262000 by 262000, and i want to know how the number of times that an eigenvalue is degenerate. I can get the eigenvalue using the arnoldi method but ...
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Optimal basis set of Gaussian functions for describing a quantum system (part 2)
It's a part 2 of this question Optimal basis set of Gaussian functions for describing a quantum system (part 1)
There, the answer was given to a question related to finding geometric progressions of ...
- 1,753
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Solving a matrix pencil (quadratic eigenvalue) problem with Mathematica
According to Wikipedia
The matrix pencil of degree $\ell$ is the matrix-valued function
defined on the complex numbers $L(k) = \sum_{i=0}^{\ell} k^{i} A_{i}$.
Here $A_{\ell}$ are non-zero $n\times n$...
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2
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Optimal basis set of Gaussian functions for describing a quantum system (part 1)
This question arose during the discussion of the previous questions: Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set? and Finding excited states ...
- 1,753
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Step by Step for Generalized Eigenvectors?
When I do
WolframAlpha["Eigensystem[{{1,-3},{3,-5}}]", PodStates -> {"Step-by-step solution"}]
It only shows steps for non-generalized ...
- 3,044
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2
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Finding excited states using the condition of wave functions orthogonality
This is the continuation on my previous question Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set?
Brief description of the problem: I would like ...
- 1,753
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Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set?
I have a basis set that describes with high accuracy the ground state of this system:$$H=-\frac{1}{2}\Delta-\frac{1}{r}+\frac{25}{8}\rho^2-5/2$$where $r=(\rho,z,\phi)$ is a coordinate in the ...
- 1,753
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1
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Plot of the real part of the maximum eigenvalue of matrix
I am looking to plot the real part of the maximum eigenvalue of matrix A as a function of x and y.
Thanks
...
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1
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How to expand the existing basis set so that it becomes more complete?
I have a set of anisotropic gaussian basis set which describes the ground state of the system with great accuracy.
The Hamiltonian of the system has the following form: $$H=-\frac{1}{2}\Delta-\frac{1}{...
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vote
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Automatically obtain feature equations
How can I automatically obtain the characteristic equation of a second-order differential equation given any expression?
Assuming a second-order differential equation is given as follows：
...
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0
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Complex eigenvalue of a symmetric matrix
I am working on a eigenvalue problem. I am using Eigensystem
However, I am facing issues when I change the input parameters:
I get complex eigenvalues. I couldn't understand the reason although my ...
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1
answer
44
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Renaming terms of the eigenvalues of a matrix
I have a matrix (DpT2) with complicated eigenvalues that I'm hoping to simplify.
...
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2
votes
1
answer
78
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Verify that the eigenvector is the eigenvector corresponding to the eigenvalues [closed]
I saw similar questions on the forum, but I still have some doubts. I use a more general form of symbol matrix A to verify that the eigenvector is the eigenvector corresponding to the eigenvalues. The ...
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How to sort the eigenvalues and the eigenvectors in such way that each eigenvalue to its own corresponding eigenvector? [closed]
I would like to find eigenvalues and the corresponding eigenvectors of the matrix AA.
...
- 1,753
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1
answer
128
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Solve computes discontinuous eigenvalues of parameter-dependent matrix
So I have a family of unitary matrices $m(x,y)$, which depend on two parameters $x,y \in [0, 2 \pi)$. Its eigenvalues should be continuous in $(x,y)$. Since $m(x,y)$ is a unitary matrix, its ...
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How to find the common eigenvectors of these commuting matrices?
Given matrices P and Q defined as
P = {{x - I y, z}, {z, x + I y}}; Q = {{0, 1}, {1, 0}};
...
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votes
1
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Troubling using the arnoldi method
I have the following code:
The first part is just defining the matrices, the error is at the end of the code.
...
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7
votes
1
answer
701
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Is there a bug in Eigensystem[]?
Does Eigensystem[] produce incorrect output for symmetric matrices with integer components?
The following eigensystem decomposition of a 12x12 matrix and its ...
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0
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51
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Automatization of eigenvalue analysis
I am trying to make a code to extract the eigenvalues of an eigenfunction of an ODE, and then insert these eigenvalues in an operation.
I start with the following, where sol is the eigenfunction of ...
- 561
1
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1
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90
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Why is generating normalized random $1000 \times 1000$ matrices and plotting the eigenvalues so slow?
For each of the distributions $N(0,1)$ and $\pm 1$ equal probability and for each of $N \in \{5,10,20,50,100,200,1000\},$ I want to generate an $N \times N$ matrix with entries chosen from the ...
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