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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8
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1answer
96 views

Inconsistent behaviour between Active and Inactive forms of PDEs (finite element method)

I have been using the finite element tools in Mathematica version 13.0 to solve eigenvalue problems in physics (Schrödinger equation) using NDEigensystem, but I am having some issues with non-...
1
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1answer
69 views

How to give range of values while using NDEigensystem for a 2D Schrödinger equation?

This program runs fine and I am able to get eigenvalues and eigenfunctions, however, I want to give a range of values for x and y. Can you suggest, how to edit my code for that? ...
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0answers
41 views

Eigenvalues and vector of a complex matrix seems to be wrong! [closed]

I am calculating the eigenvalues and eigenvectors of a matrix ...
0
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0answers
125 views

Could all eigenvalues of this matrix be positive?

I have the following list $\beta$ with 5 equations ...
0
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1answer
62 views

How to use NDEigensystem to find eigenfuction and Eigenvalues of 1D Harmonic Oscillator? [closed]

Where am I wrong? Eigenfunctions and Eigenvalues are coming out fine, but while doing the integration, I am facing difficulties. ...
3
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2answers
144 views
5
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0answers
87 views

Does current Mathematica capability allow solving PDEs (e.g. reaction diffusion equation) over surface of a mesh or surfaces

I came across this nice paper (https://arxiv.org/pdf/1605.01583.pdf) where the authors simulated a reaction diffusion system over the surface of a gecko, primarily to understand how various patterns ...
2
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3answers
170 views

Eigenvalue problem with NDSolve

I am trying to solve the following system of linear ODEs. It is an eigenvalue problem. ...
0
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1answer
49 views

List of eigenvalues of a list of abstract states

Suppose I have the states \Psi, \Phi and \Zeta and I also have the following relations given ...
2
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1answer
99 views

Solving boundary value problem with coupled odes at interface

I am trying to get the eigenvalues of the following differential system ...
2
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1answer
61 views

How to find the characteristic vibration frequencies of a system with any number of masses and springs using eigendecomposition?

I have created a program to solve any system of three springs and two masses using Mathematica's Eigendecomposition functions. My goal is to solve a generalization of the spring system presented in ...
4
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1answer
70 views

Using the result of NIntegrate as a potential in NDEigensysem

I am trying to find the eigenvalues and eigenstates of a Hamiltonian with a potential which cannot be analytically defined. In particular, it is the integral of the product between two functions: <...
1
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1answer
64 views

How to improve accuracy of calculating eigenvalues of Non-Hermitian matrix?

I have a non-Hermitian Matrix nonHM whose size is $n \times n$ and is a function of $c1$.the Eigenvalues are symmetric with ...
15
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2answers
323 views

Library for FEAST method is missing

Mathematica (V 12.3.1, Native Mac M1 version) is not letting me use the FEAST method for solving eigenvalue problems. For example, ...
2
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2answers
109 views

Find relationship between parameters to prove conditions of eigenvalues

I have the following 3-by-3 matrix. I need to find condition(s) on the parameters 'a' and 'b' such that this matrix has exactly 1 eigenvalue bigger than 1 in absolute value and other two eigenvalues ...
13
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3answers
552 views

Routh-Hurwitz criterion not giving correct answer when done manually?

Consider the system: \begin{align} \frac{dS}{dt} &= \nu N -\frac{\beta S I}{N} + \xi R - \nu S\\ \frac{dE}{dt} &= \frac{\beta S I}{N}- \sigma E -\nu E \\[2ex] ...
1
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0answers
23 views

'Tag in is protected' error in eigenvaules for large size Hamiltonian [closed]

I am trying to compute the eigenvalues for any size Hamiltonian matrix. To do this, I first manually compute the first few cases for N=2,3. However, when I want to see what happens for N=4, I meet ...
1
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1answer
61 views

Obtaining more values from `NDEigenvalues`

When I run this code ...
0
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1answer
65 views

Construct a matrix from its elements and solve the eigenvalue problem

I want to construct a 10 by 10 matrix whose elements are given by $$ H_{nm}=\delta_{nm}\left (n^2+v[b_1-b_0-h(2m,b_0,b_1)]\right) \\ +v(1-\delta_{nm})\left (h(n-m,b_0,b_1)-h(n+m,b_0,b_1)\right) $$ ...
0
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1answer
75 views

Problem with the plots of eigenvalues of the Matrix

I am trying to plot the eigenvalues of the following matrix ...
2
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1answer
29 views

Using Maximize function with UnitaryMatrixQ constraint

Define a function ...
2
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0answers
48 views

NDEigensystem potential with a singularity

Consider the following eigenvalue equation $$-\frac{d^2}{dx^2}\Psi_n(x)+\left(gx^4+\frac{1}{x^2}\right)\Psi_n(x)=E_n\Psi_n(x),\qquad x\in(-10,10),\qquad\Psi(-10)=\Psi(10)=0$$ The boundary of $x$ is ...
2
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1answer
63 views

Custom Normalization for NDEigensystem

I am trying to solve the Laplace equation in polar coordinates $$-\left(\frac{\partial^2\psi_n(r,\theta)}{\partial r^2}+\frac{1}{r}\frac{\partial\psi_n(r,\theta)}{\partial r}+\frac{1}{r^2}\frac{\...
2
votes
1answer
142 views

define edge set of a graph

I want to define a graph in Mathematica which its vertex set is cartesian product of two sets. I define the vertex set by Tuple[] but two vertices are adjacent if and only if the intersection of the ...
1
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1answer
81 views

Find interval/range of certain coefficients to prove conditions of eigenvalues

I have seen similar questions to the one I am posting here, but I haven't been able to execute it on Mathematica. I would request some help with the following: I have the following matrix: ...
3
votes
1answer
155 views

Eigenvalues of $i x^3$ potential

There is a famous paper by Carl Bender et al., where they investigated a class of non-Hermitian potentials and showed their spectrum is entirely real. One such a case is $i x^3$ potential. I would ...
0
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0answers
44 views

Indexing of NDEigensystem Result on a Cluster

I am trying to run on a cluster (where the version 11 of Mathematica is available) a code involving the following calculation: ...
0
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0answers
104 views

How to implement the symplectic transformation in Mathematica?

Consider a $4\times 4$ matrix $A$, which can be diagonalized by a symplectic matrix S such that $$A = SA_d S^T$$ where $A_d = \oplus_{k=1}^{2} a_k \mathbf{I}$ where $a_k$ is the $k$-th symplectic ...
7
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0answers
135 views

How to compute eigenvalues of linear function (not matrix)?

How to compute eigenvalues of a known linear function? In Julia, there is a package https://jutho.github.io/LinearMaps.jl/dev/ to compute the matrix representation of given function, then we can ...
4
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0answers
95 views

How to use NDEigenvalue to accurately estimate functional determinants?

Goal: Ultimately, I would like to find a trustworthy approximation for the ratio of the functional determinant of two differential operators using the formula $$ \frac{\text{Det}[\hat{D}_0]}{\text{Det}...
3
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0answers
91 views

(Possibly bugs? ) Wrong results provided by `DEigensystem`

I was trying DEigensystem with the following code: ...
2
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1answer
56 views

NDEigensystem convergence and comparison to DEigensystem

Consider the following eigenvalue differential equation $$ -u_n''(x)+x^2u_n(x)=E_nu_n(x),\qquad x\in(-\infty,\infty). $$ If you know a little bit of physics, you would know that this is the ...
4
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0answers
62 views

Finding matrix in Krylov subspace (Lanczos method)

The Lanczos method for finding the smallest eigenvalue of a hermiteian matrix $H$ is based on the construction of a vector subspace (Krylov space) where one can build a matrix $H_{Krylov}$ which is ...
0
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0answers
56 views

NDEigensystem eigenvalue convergence problem

I am solving an eigenvalue equation (a time independent schrödinger equation) and want to find the eigenvalues ...
0
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1answer
44 views

Plotting Triplet Points with Unique Colors for Each Point

I have a set of eigenvalue triplets from some 3x3 matrices and I would like to plot them on the complex plane. My goal is to plot them such that each triplet has a unique color that identifies the ...
1
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1answer
46 views

A quadratic system with two solutions which may be solved with numeric coefficients, but not with symbolic ones

The system below may be solved using the observation that the second and third equation admit solution (,0,0,); alternatively, the determinant of these two equations must be 0. ...
4
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1answer
126 views

Eigenvalue and SparseArray

This the code of Hofstadter spectrum for square lattice using Mathematica ...
2
votes
2answers
63 views

How can I store vectors in a matrix

I am triying to generate realizations of a Gaussian random process using the KL expansion. For that, I need to multiply an eigenvector for an eigenvalue and a random variable. I have tried ...
2
votes
1answer
123 views

Solving simultaneous differential equations using eigen value method

I wish to solve the following set of ODE. $$i\frac{d}{dt}B_{n}\left(t\right) =f\sqrt{\left(P-n\right)\left(n+1\right)}B_{n+1}\left(t\right)+f\sqrt{n\left(P-n+1\right)}B_{n-1}\left(t\right) + Y\left[...
1
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0answers
46 views

NDEigensystem solutions depend on how many solutions I ask for?

Background I am using NDEigensystem to solve the following eigenvalue problem: $$ \left( \begin{matrix} m&-i\partial_x \\ -i\partial_x & -m\end{matrix}\right) \left( \begin{matrix} u_u(x) \\ ...
3
votes
0answers
191 views

Chladni experiment verification

I refurbished my post in order to be more understandable. After computing simulations of Chladni patterns with Mathematica (see my previous topics), I finally went to practice. I realized my own ...
0
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0answers
76 views

How to find eigenvalues of 8x8 matrix?

I am new to Mathematica, and was trying to find the eigenvalues of an 8x8 matrix using Mathematica. I have fairly simplifies the matrix A into a mathematical expression and I know the final ...
0
votes
1answer
43 views

Mathematica returns an empty plot for the real part of the eigenvalues [closed]

I have a 3*3 matrix. Using Mathematica I have found the eigenvalues in terms of "K". The problem arises when I'm plotting the real part of eigenvalues against "k" (k is a positive ...
4
votes
2answers
126 views

How to generate the 8^th order symmetric binary matrices whose sum of absolute eigenvalues is 8?

It is needed to generate all 8th order(8 by 8) symmetric binary matrices(of 0's and 1's) such that the sum of the absolute eigenvalues is 8. Listing all the 8th order symmetric binary matrices and ...
6
votes
2answers
220 views

2D Chladni patterns realistic animation

My wish is to create a (realistic) animation of the patterns appearing during the Chladni experiment. I tried something, but it is not continuous because it is based on the eigenmodes, so the ...
1
vote
0answers
46 views

Eigenvalues of a 6x6 matrix [duplicate]

Eigenvalues[{{0, A, 0, B, 0, D}, {-A, 0, -C, 0, -EE, 0}, {0, C, 0, A, 0, B}, {-B, 0, -A, 0, -C, 0}, {0, EE, 0, C, 0, A}, {-D, 0, -B, 0, -A, 0}}] I am ...
0
votes
1answer
73 views

NDEigensystem does not evaluate

I am trying to obtain the eigenvalue of a certain $4\times 4$ matrix differential operator. The region I consider is a rectangle of size $5\times 200$. At left and right side, I applied the periodic ...
0
votes
1answer
61 views

Number of elements in a list [closed]

I have written the following program in mathematica. ...

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