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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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Kernels die running parallel Eigensystem[]

I am diagonalising random (real) symmetric matrices M of sizes N up to $\sim 10^3$, doing it around $5.10^4$ times. For $N\ge330$, some kernels seem to die during the evaluation of Eigensystem[M] in ...
Kaio's user avatar
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2 votes
3 answers
486 views

Why is Mathematica not simplifying eigenvalues?

For matrix A = {{x*Exp[I*y], z}, {z, x*Exp[(-I)*y]}}; , Mathematica yields the following eigenvalues: ...
Jee's user avatar
  • 386
1 vote
1 answer
55 views

Arnoldi method for generalized eigenvalue problem with sparse matrices

I would like to solve a generalized eigenvalue problem involving sparse matrices using the Arnoldi method. I would like to use the Arnoldi method in the hope of speeding up the calculation. Problem is,...
coussin's user avatar
  • 361
3 votes
2 answers
95 views

Does NDEigensystem work in dimensions greater than 3?

I have been trying to run NDEigensystem on a differential operator with four variables $\alpha$, $\beta$, $\gamma$, and $\delta$. I've found that if I run the ...
NOABM's user avatar
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1 vote
0 answers
96 views

Speed up the evaluation of two million consecutive eigenvalues using `NDEigenvalues`?

$Version "13.0.1 for Linux x86 (64-bit) (January 29, 2022)" I have $28$GB of RAM. I need to calculate two million consecutive eigenvalues for a given ...
user444's user avatar
  • 2,446
5 votes
2 answers
116 views

Improving a plot of eigenvalues versus a parameter obtained by ListPointPlot3D

I have a bunch of $m \times m$ matrices with $m\geq 2$, which I would like to plot their eigenvalues as a function of a parameter. These eigenvalues are usually complex and wind together as a function ...
Shasa's user avatar
  • 1,043
5 votes
1 answer
97 views

Alternative Representation for Energy Levels and Energy Level Density (II)

Following my previous question, I want a graph that must look like this (the lower image is taken from the Wikipedia page for the Microcanonocal Ensemble-->> Quantum Mechanical), The code for ...
user444's user avatar
  • 2,446
0 votes
0 answers
44 views

Inner working of `NDEigensystem` [duplicate]

What is the inner workings of the NDEigensystem? How does it solve a second-order differential equation? I know it is an inbuilt Mathematica function. I want to ...
user444's user avatar
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0 votes
0 answers
58 views

Underflow using Eigensystem for large mass and stiffness matrix with large stiffness values

I am trying to use the Eigensystem command to determine the eigenvalues and eigenvectors of a multi-degree of freedom system. Currently, I have a mass matrix and a ...
Panagiotis Andreou's user avatar
1 vote
1 answer
97 views

How to find periodic steady state of symbolic matrix in Mathematica?

I am currently trying to recreate results in a paper where I solve for the periodic steady state of the following rate matrix: Where epsilon is some force parameter, I have found the left and right ...
magg13__'s user avatar
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0 answers
65 views

How to find linearly dependent eigenvectors of non-diagonalizable matrix (with exceptions)?

Here is the code to produce a $9\times9$ matrix: ...
ZHENGYAO HUANG's user avatar
0 votes
1 answer
127 views

Is it possible to make a phase portrait of this system?

I need help with this problem: I have this ODE system For this system, manually, I calculated the stability points, eigenvalues, and Jacobian matrix for a range of ALPHA values (I considered those ...
Victor Pinto Msc Student's user avatar
2 votes
0 answers
62 views

How to get single $n^{th}$ eigenvalue and eigenfunction using NDEigensystem?

I am trying to solve the Schrödinger equation for a $2D$ Harmonic Oscillator using the following codes. Code-1 ...
user444's user avatar
  • 2,446
1 vote
1 answer
49 views

How to find the Eigenvalues for complicated Bessel boundary value problem?

I am trying to find energy eigenvalues in a problem. A function depends on the radius R (of a quantum dot) and the energy. The function was obtained from matching wavefunctions at the boundary of the ...
Rainforest Frog's user avatar
1 vote
1 answer
67 views

Using ParametricNDSolve does not work for certain parameters

I want to solve the following second-order DE $$ \ddot{w}(t) H(w(t))+\frac{1}{2}(\dot{w}(t))^2 H'(w(t))+g(w(t))(c_0 (\overline t-\underline t)-w(t)) =0, $$ with boundary conditions $\dot{w}(\overline ...
Jerome P.'s user avatar
1 vote
0 answers
37 views

Using DEigensystem with parametrized cuboid

The following code where Cuboid has a predefined dimensions {1, 1, 1} works fine: ...
Mirko Aveta's user avatar
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3 votes
1 answer
114 views

NDEigensystem does not work when using nonlinear operator [closed]

I am trying to find the eigenvalues of the stationary Gross Pitaevskii equation using the NDEigensystem command via ...
user3623974's user avatar
0 votes
0 answers
84 views

Break symbolic eigenvalue calculation early

I am computing eigenvalues of matrices with single monomial entries (x,y,z, etc.) and for efficiency, need to truncate calculations early if any eigenvalues contain non-linear (x^{2}, \sqrt(x),x*y etc....
JJJJJJJJJJJJJJJJ's user avatar
3 votes
1 answer
147 views

Dirac equation for a Coulomb potential in 2D with 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 ...
AminD's user avatar
  • 51
2 votes
1 answer
198 views

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 ...
AminD's user avatar
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1 vote
0 answers
90 views

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 ...
Victor Pinto Msc Student's user avatar
0 votes
1 answer
90 views

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 ...
mathetronaut's user avatar
1 vote
0 answers
115 views

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)...
Sprog's user avatar
  • 179
0 votes
0 answers
37 views

Root function in the output [duplicate]

I was calculating the eigenvalues of a matrix and the output contained some eigenvalues like: ...
MSHD's user avatar
  • 21
1 vote
1 answer
93 views

How can I use Gaussian elimination for finding QNMs in this code?

I am reading the article Scalar-gravitational perturbations and quasinormal modes in the five dimensional Schwarzschild black hole. I want to reproduce the value of the quasinormal frequency with $l=2,...
amon xu's user avatar
  • 41
1 vote
1 answer
69 views

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 ...
Gae P's user avatar
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4 votes
3 answers
112 views

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 ...
Victor Pinto Msc Student's user avatar
3 votes
1 answer
60 views

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 ...
cconsta1's user avatar
  • 155
2 votes
1 answer
342 views

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 ...
user444's user avatar
  • 2,446
3 votes
2 answers
109 views

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 ...
noodles's user avatar
  • 31
1 vote
0 answers
73 views

Eigenvectors of a matrix (Solving and Plotting)

Given a nxn matrix h[k] ...
Med Ch's user avatar
  • 117
0 votes
0 answers
51 views

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} })] ...
MMA13's user avatar
  • 4,732
3 votes
2 answers
149 views

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. &...
Shasa's user avatar
  • 1,043
0 votes
0 answers
46 views

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 ...
Mateus Rocha's user avatar
0 votes
1 answer
140 views

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 ...
Mam Mam's user avatar
  • 1,863
2 votes
2 answers
69 views

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} ...
Andreas132's user avatar
1 vote
0 answers
41 views

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: ...
ZDZ's user avatar
  • 11
1 vote
1 answer
95 views

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 ...
user199's user avatar
  • 71
0 votes
1 answer
92 views

How should a function written through the Module be written in the FindMinimum correctly?

There is a function that is written using a module ...
Mam Mam's user avatar
  • 1,863
1 vote
1 answer
55 views

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 ...
Mam Mam's user avatar
  • 1,863
0 votes
1 answer
77 views

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 ...
qising's user avatar
  • 43
2 votes
1 answer
98 views

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 ...
Mam Mam's user avatar
  • 1,863
2 votes
1 answer
155 views

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 ...
F.Mark's user avatar
  • 599
1 vote
1 answer
124 views

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, ...
Mam Mam's user avatar
  • 1,863
4 votes
2 answers
210 views

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 ...
Mam Mam's user avatar
  • 1,863
4 votes
3 answers
301 views

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 ...
Young's user avatar
  • 7,495
1 vote
1 answer
148 views

Displaying NDEigensystem Results

I want to display a collection of deformed meshes in a GraphicsGrid where the surface colors are proportional to the displacement. ...
Young's user avatar
  • 7,495
0 votes
1 answer
70 views

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 ...
LittleBlue's user avatar
1 vote
1 answer
78 views

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 ...
Mam Mam's user avatar
  • 1,863
6 votes
0 answers
194 views

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 $n\times n$...
Rob's user avatar
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