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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3
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2answers
128 views

Asymptotic law in Laplace's problem

$\textbf{Eigenvalue problem on a unit square $\Omega = [0,1]^2$ :}$ Consider the eigenvalue problem with the Dirichlet boundary condition that is, $$-Lu = \lambda u$$ where $$L = \frac{\partial^2}{\...
0
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0answers
39 views

Enforcing Vanishing Dirichlet Boundary Conditions While Computing Spectrum via Arnoldi Method [closed]

I want to compute an estimate of the spectrum for a free particle inside a tetrahedral box. Thus I computed the discretized Laplacian for the interior of a tetrahedron and its boundary. Using this ...
3
votes
1answer
133 views

Solving a Eigenvalue Problem

$\textbf{Eigenvalue problem on a unit square $\Omega = [0,1]^2$ :}$ Consider the eigenvalue problem with the Dirichlet boundary condition that is, $$-Lu = \lambda u$$ where $$L = \frac{\partial^2}{\...
3
votes
1answer
148 views

How can I use Tally in my code?

I a computing the eigenvalues and eigenfunctions of a Laplacian on a unit square. I have written it as follows: ...
0
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1answer
66 views

How to write matrix elements in Mathematica? [closed]

For a matrix $A$, one computes the $ij$-$th$ matrix elements in a basis $\{|e_i\rangle\}$ as $$A_{ij} = \langle e_i|A|e_j\rangle$$ How can one implement this in Mathematica? As an example, consider a ...
0
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0answers
15 views

QR algorithm implementation for eigensystem - where is error [duplicate]

I implemented the simplest possible program of QR algorithm, but the program gives wrong solutions, i.e. eigenvalues (diagonal elements of converged matrix x) and ...
1
vote
1answer
141 views

Program for computing Weyl's law

I have calculated the solution to the Laplacian eigenvalue problem on the unit square $\qquad - \Delta u(x,y) = \lambda u(x,y) \text{ on } {[0,1]}^2$ with the Dirichlet's boundary condition ($u = 0$). ...
4
votes
1answer
43 views

Removing Sharp Peaks from NDEigensystem Results

I have an eigensystem I am trying to solve using NDEigensystem, so as a test I am using a different operator which is known to admit to analytical solutions which are smooth(i.e., no discontinuities ...
0
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1answer
47 views

How I can find the eigenvalues and eigenvectors of 500 matrices with 3x3 dimensions? [closed]

I can apply the Eigensystem command to a single matrix and it worked fine. But it takes me too much time. I want to get the eigenvalues and eigenvectors of multiple 3x3 matrices at the same time. ...
2
votes
3answers
30 views

Repeated ReplacePart On Each Element of a Square Matrix for Eigenvalue Difference

I have a large $n\times n$ square matrix, whose elements are all either 0 or 1. I want to see by how much the single largest eigenvalue of the matrix (which Mathematica gives as the first element in ...
3
votes
2answers
287 views

Speedup calculation of the largest eigenvalue and eigenvector of a 400×400 matrix? [duplicate]

Actually, the matrix is an adjacency matrix of a network. The code is: ...
3
votes
1answer
64 views

Getting different eigenvectors for same matrix? [closed]

I have the same two matrices, one has the input values as integer and the other as real numbers. Mathematica shows the eigenvectors are completely different for the two same matrices and wondering ...
7
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4answers
261 views

FindInstance won't compute this simple expression

I want to find instances where this standard 3x3 symmetric matrix has only positive eigenvalues. So I run ...
5
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1answer
101 views

How to compute the trace distance of a density matrix

I am trying to compute the trace distance of two general $4 \times 4$ density matrices as such: $D=\frac{1}{2} \, \mathrm{tr} \, |\Delta\rho|_1$ where $\Delta\rho$ is the difference between two ...
1
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1answer
43 views

Ordering eigenvectors for basis transformation

Let's say I have a matrix $H$ represented in some basis, $a$, and I'd like to transform this to be represented in a different basis, $b$. The only difference between the bases is that $b$ is a basis ...
2
votes
1answer
155 views

Numerical solution of Eigenvalue equation

I am interested in finding eigenvalues of Schrödinger-type equations, a prototype example being $$- w^{\prime \prime } (y) - 6 \operatorname{sech}^2 (y) w(y) + w(y) = \lambda w(y)$$ I posted a ...
7
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0answers
195 views

Numeric Solution Hydrogen Atom

I'm trying to solve the Schrödinger equation for the hydrogen atom without made the variable separation of the polar and radial coordinate. It is my test code to extrapolate to another system with its ...
3
votes
3answers
293 views

Solving a Sturm-Liouville problem

Ello, I would like to reproduce the analytical solution of the following eigenvalue problem, or at the least confirm them numerically (especially the eigenvalues): $$ - \frac{1}{2} y^{\prime \prime} ...
0
votes
1answer
47 views

Plot Eigenvalues with respect to a parameter

I have a parametrical matrix (18x18) which I want to plot its eigenvalues with respect to a parameter. For simplicity, lets assume that it is instead a 3x3 matrix which is not fully numerical but ...
1
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1answer
72 views

Lowest Eigenvalue of a large sparse matrix without choking up the RAM (Corrected) [closed]

I am trying to find the lowest eigenvalue of a large sparse matrix of dimension N (=$3^n$, where n is number of particles in system ) using ...
4
votes
1answer
74 views

Sort eigenvectors by eigenvalue and assign to variables

I have the following question: Let T = {{0, 0, 2}, {0, 0, 0}, {2, 0, 3}}, I know that its eigenvalues, in a decreasing order, are 4, 0 and -1. Mathematica displays ...
1
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0answers
29 views

How to speed up this code (finding eigenvector with smallest eigenvalue)? [closed]

I have following code. The function TraceSystem is to take partial trace of matrix and I think this part is fine. The main code is below in dd and I think the main problem is in here for Eigenvector. ...
0
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0answers
24 views

Solving quadratic eigenvalue problem [duplicate]

I am trying to solve a quadratic eigenvalue problem using Mathematica similar to Matlab command "polyeig" https://www.mathworks.com/help/matlab/ref/polyeig.html How to do it using ...
2
votes
0answers
60 views

What is the fastest way to get the lowest eigenvalue and corresponding eigenstate in Mathematica?

I tried to use the Arnoldi method to get the smallest eigenvalue and corresponding eigenstate for large matrix. However, Arnoldi did not give me the desired result: ...
3
votes
2answers
147 views

NDEigensystem and radial function equation for Hydrogen atom

I'm trying to numerically solve the radial equation for the 3D hydrogen atom problem, i.e., to find $R(r)$ which satisfies: $$ -\frac{\hbar^2}{2m}\left[\frac{1}{r}\frac{d}{dr}\left(r^2\frac{dR(r)}{dr}\...
-2
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1answer
48 views

Sorting of eigensystem accroding to specific eigenvector

I have a matrix, I want to sort it with respect to specific eigenvectors. Here, I provided an example of a matrix HT: ...
0
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1answer
86 views

Having problem in evaluating the eigenvalues of an $11\times11$ symmetric matrix in Mathematica [closed]

I am solving an $11\times11$ matrix in Mathematica. I am facing problem when I try to find the determinant or eigenvalues of this matrix. The error (Det::matsq/<...
8
votes
2answers
195 views

Why Mathematica gives wrong eigenvalues for this equation?

Here is an eigenvalue problem in cylindrical coordinate: $$\mu(r)\frac{\partial}{\partial r} \left( \frac{1}{\mu(r)}\frac{1}{r}\frac{\partial (ru)}{\partial r} \right)=-p^2u$$ where p is the required ...
2
votes
1answer
99 views

Sorting Eigensystem According to Complicated Rule

I have looked for an answer to this but the near duplicates I could find seemed slightly distinct. I have a matrix $A$ which has eigenvalues in pairs $\lambda_1,-\lambda_1,\lambda_2,-\lambda_2,\dots$. ...
0
votes
1answer
46 views

Why is Mathematica not simplifying further even after providing assumptions?

m = {{0, 0, 1, 0}, {0, 0, 0, 1}, {-5 X^2, X^2, 0, 0}, {X^2, -X^2, 0, 0}}; Simplify[Eigenvalues[m], Assumptions -> X>0] The output I get is this below. The ...
0
votes
1answer
88 views

Transforming a full $4\times4$ symbolic matrix into a full $3\times3$ matrix and an eigenvalue

I have a $4\times4$ matrix A=\begin{pmatrix} 0.16 (\cos (\text{kx})+2) & 0.55 \cos \left(\frac{\text{kx}}{2}\right)+(0.\, +0.76 i) \sin \left(\frac{\text{kx}}{2}\right) & 0.55 \cos \left(\...
2
votes
1answer
96 views

NDEigensystem to solve differential equation

When trying to solve the differential equation radialEqdouble[k_] = f''[u] + k*u^2*f[u] - u^4*f[u] where k is a constant, I am able to produce a plot consistent ...
4
votes
2answers
164 views

eigenvalue and eigenfunction of complex euler-bernoulli beam

So I am new to Mathematica and am trying to solve the euler-bernoulli modal equation for a U-shaped Cantilever beam given by equations :- where i is the index of the region. In total there are 2 ...
1
vote
1answer
57 views

Sorting the eigensystem of a symbolic matrix

My symbolic matrix $A$ reads \begin{equation*} \left( \begin{array}{ccc} a \left(x^2+y^2+z^2\right) & b y z+i v x & -i v y \\ b y z-i v x & a \left(x^2+y^2+z^2\right) & b x y+i v z \\...
0
votes
1answer
61 views

How can I get rid of Abs?

In the following code, the functions WP[t] and WS[t] are real. Time also is a positive parameter. As you can see, MATHEMATICA enters Abs in the calculations. Including Abs only complicates the next ...
0
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0answers
36 views

how can I correct this code? [duplicate]

I need to calculate matrix m1 according to following algorithm. Then, I have to put it in the differential equation. However, matrix m1 is complex and therefore the differential equation does not work....
0
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0answers
51 views

How can I correct this code to get an answer? [duplicate]

I need to calculate matrix m1 according to following algorithm. Then, I have to put it in the differential equation. However, matrix m1 is complex and therefore the differential equation does not work....
4
votes
1answer
182 views

Solving equation in 3D

How I can solve the equation in 3D domain? According to the following post, I encounter an error when I run the program. Any help would be graet! This section should be considered as a continuous ...
0
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0answers
75 views

How to solve the following equation numerically?

In the following code, if the matrix "n = (-I*(m1)) + (m2)" in the differential equation contains only the matrix "m1", I will get the answer, but if the matrix "n" is ...
0
votes
0answers
69 views

solving a 2D eigenvalue problem for a partial differential equation

I'm fairly new to Mathematica and I'm looking for a way to solve a partial differential equation subject to periodic boundary conditions. The form of the equation looks like this: $\frac{\partial^2}{\...
1
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0answers
54 views

Strange behaviour of eigensystem

I encounter with really strange behavior in calculating the eigensystem of a hermitian matrix. I upload the matrix here. After loading it you can construct the main matrix as follows ...
3
votes
5answers
203 views

Simplifying away imaginary part

I'm solving the following eigensystem, and I get result which looks complex-valued. I expect the result to have 0 imaginary part, can anyone see a way to simplify it away? ...
2
votes
1answer
62 views

Generate constraints that ensure positive definiteness

What is a good way to generate algebraic constraints that ensure matrix be positive definite? Ideally, I'd be able to do something like below ...
0
votes
2answers
46 views

Problem for defining continously Eigenvectors from Kane and Mele model

The model is a simple eigenvalue problem. A matrix that depends on some parameters kx, ky, t, defined by: ...
2
votes
0answers
47 views

Determine a negative semidefinite 5*5 matrix

I'd like to find the real parameters $\left\{p,\alpha ,a_{24},c_3,c_7,c_9,c_{10}\right\}$ in $M$, which is a $5\times 5$ real symmetric matrix, such that $M$ is negative semidefinite. My code for $M$: ...
1
vote
1answer
59 views

Determine a positive semidefinite 5*5 matrix

I'd like to find the real parameters $\left\{a_{14},c_6,c_8,c_{10},c_{12},c_{13},c_{14},c_{15},\alpha \right\}$ in M, which is a $5\times 5$ real symmetric matrix, such that M is positive semidefinite....
4
votes
1answer
101 views

Different results in DEigensystem compared to NDEigensystem for Laplacian eigenvalue problem (-Δu=λu) on unit square

I want to calculate the solution to the Laplacian eigenvalue problem on the unit square with trivial Dirichlet boundary conditions: $$- \Delta u(x,y) = \lambda u(x,y) \text{ on } {[0,1]}^2$$ with $u(0,...
5
votes
0answers
53 views

Effectivelly using Compile for calculate a Unitary transformation

I am new to Mathematica, and this is my first post, so if my question is not clear enough, I would be glad to read the comments and edit my question to add more information. The problem I need to ...
3
votes
1answer
162 views

Plotting Eigenvalues and severe Noise Problems

I am trying to plot Eigen values of my System Hamiltonian in Mathematica. This is generating very noisy plot. This is my code. ...
1
vote
2answers
74 views

Integrate over one variable of a 2D interpolating function returned from NDEigensystem

I'm trying to implement the answer for "Integrate only one variable of a 2D interpolating function" (https://mathematica.stackexchange.com/a/161962/73672) but for interpolating functions ...

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