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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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 ...
• 21
1 vote
82 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 ...
81 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 ...
• 124
1 vote
86 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)...
• 179
37 views

Root function in the output [duplicate]

I was calculating the eigenvalues of a matrix and the output contained some eigenvalues like: ...
50 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 ...
• 617
105 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 ...
57 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 ...
• 155
214 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 ...
• 1,554
102 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 ...
• 31
1 vote
61 views

Eigenvectors of a matrix (Solving and Plotting)

Given a nxn matrix h[k] ...
• 117
50 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} })] ...
• 4,265
146 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. &...
• 801
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 ...
• 143
132 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 ...
• 1,753
59 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} ...
• 103
1 vote
35 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: ...
• 11
35 views

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. ...
• 899
1 vote
89 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 ...
• 71
88 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 ...
• 1,753
1 vote
52 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 ...
• 1,753
74 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 ...
• 43
94 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 ...
• 1,753
109 views

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