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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Is it possible to find eigenvectors of matrix $f(1)$ in the given code analytically in terms of the variable $y$?
I have this differential matrix equation f'[x] == {{2 x, y + 5 I}, {-3 I + 2 y, Sin[3 x] - 5 y}}.f[x] for f[x] with the initial ...
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Can't evaluate and plot eigenfunctions after using NDEigensystem
I used NDEigensystem for finding eigenvalues and eigenfunctions of specified dif. operator. If I set R=1 everything is good and I get right results, but when I set R=10 and more I get complex ...
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Using NDEigensystem for infinite interval
I'm trying to find eigenvalues and eigenfunctions for a differential operator H=p''[x]-V[x]*p[x]. Actually, V[x] is a potential (...
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Construction of RMT Hamiltonian with given potential
It is well known that the Random Matrix Theory (RMT), the potential function for the Gaussian ensembles, is
$V(H) = \frac{1}{2} H^2 \quad \Rightarrow \quad P(H) \propto e^{-\frac{N}{2} \operatorname{...
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Find parameters b, c in a parameterized matrix A(b,c) to match two smallest eigenvalues to target values
I have matrix A that is dependent on two parameters b and c, so A = A(b,c). I need to find values for parameters b,c so that two smallest eigenvalues of my matrix A will be some exact numbers (in my ...
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Solve the 2D wave equation over a nonregular defined region
Need to find eigen values for a rectangular region simple supported membrane. I am able to get results with a uniform area - The answer is close to what I expected
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Mid Spectrum Entanglement Entropy Of Spin-chain
I want to reproduce Fig. 2(a) from https://arxiv.org/pdf/2403.09608 and Figs corresponding to EE and participation ratio from https://github.com/fabienalet/HKU-MBL/blob/main/Notebooks/...
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Eigenvalues[{A, B}] is slower than Eigenvalues[LinearSolve[B, A]] for generalized eigenvalue problems
Eigenvalues[{A, B}] is the standard usage for solving the generalized eigenvalue problem $Ay=\lambda By$.
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Overload Issue with Solving Schrödinger Equation in Mathematica [closed]
When attempting to calculate the Franck Condon Factor for a molecule, I am encountering an issue calculating the higher vibrational levels of the molecule (which is integral to my analysis of the ...
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Highly oscillating solutions of NDEigensystem
I'm trying to solve an eigenvalue problem involving the following two equations:
$$u'(r)=\Bigl[g_\pi\pi(r)-g_\rho\rho(r)\Bigr]u(r)+\Bigl[-\epsilon--g_\pi\sigma(r)+\frac{g_\omega}{3}\omega(r)+\frac{g_\...
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Issue with Interpolated Potential for Time-Independent Schrodinger Equation
I am attempting to use an interpolated potential for a molecule, initially in the form of (x, V(x)), as input for solving the Time Independent Schrodinger Equation.
After defining the data points, ...
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Seeking Recommendation on Time-Independent Schrödinger Equation Solving Method in Mathematica
I am seeking to solve a Time-Independent Schrödinger Equation using the Mathematica Platform. I will detail the problem below:
Scaling Constant is "K." This is calculated by the formula (2 m ...
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What is the correct and the best way of writing the this particular program? [closed]
I want to calculate the following matrix as give by equation 12 of this article
$$
F_{ab} = \sum_{i=0}^{d-1} \frac{(\partial_a \lambda_i)(\partial_b \lambda_i)}{\lambda_i} + \sum_{i\ne j, \lambda_i + \...
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Numerical integration taking too long
Evaluation of s[1,22]=-2.02009 takes too long so does c[10,.5].
My ultimate goal is to plot c[n,t] vs t
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NDEigensystem gives correct eigenvalues but wrong eigenfunctions
I am trying to reproduce Fig2(b) and 2(c) in this paper by solving Eq2 using NDEigensystem. Eq2 is a coupled ODE given as
$[\partial_x+k]B1(x)+\zeta(x)A1(x)=EA1(x)$...
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'#1^n' appearing at the solution of Eigenvalues [closed]
I have been trying to get the eigenvalue of a known Hamiltonian which is given by
By manual calculation I know that at least one of the eigenvalues is e_s but when I try to use the eigenvalue ...
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Variable-Size Matrix
How can I let Mathematica tell me that trace(Identity matrix)=n for n by n identity matrix? It's easy for human but what would a Mathematica code be?
A harder task: How can I let Mathematica tell me ...
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Efficient eigenvalue calculation of large matrix
My question is related to my issue from yesterday (Initializing very large matrices). It was recommended to use SparseArray to initialize large matrices efficiently....
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Eigensystem with a desired parametrisation
In equation (11) of this article the following matrix is given
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How to find the exact optimal bound
Is there any way to fix or revise this code to find the EXACT optimal bound, and could anyone help find the EXACT optimal bound? Thanks.
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When solving eigenvalues, what does the factor in front of the Root[] mean?
I tried to solve the eigenvalue of a matrix like this:
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Fitting Eigenvalues of a 8*8 matrix to experimental data
I have an 8x8 matrix which contains some parameters with a certain range. I am trying to fit the eigenvalues of this matrix to my experimental data with the goal of
having the best fit
extracting the ...
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Find the diagonalizing matrix for a general 2*2 real valued symmetric matrix [closed]
I have the following 2*2 real symmetric matrix. $mp$ and $mm$ are the eigenvalues. How do we find $\cos{\phi}$ and $\sin{\phi}$ in terms of the $n$, $y$, $mp$, $mm$?
$$
\left(
\begin{array}{cc}
\cos (...
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Different eigenfunctions are generated if I change the number of eigenfunctions I want to have
I was experimenting with solving differential equations using eigenfunction expansions. I was troubled by the fact that my solution was very different from the solution produced by ...
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Eigensystem running forever for large matrix sizes (numeric matrix)
I have a large (and numeric) square matrix and I wanna find all the eigenvalues and all eigenvectors.
Using Eigensystem command, I get the error message:
"Eigensystem::arhm: Because finding 1600 ...
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