New answers tagged eigenvalues
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Solid Mechanics FEM Simulation with Different Material Properties
This is probably something that should be shown in the documentation and I'll add this. Here is how to do it. The compliance matrix needs to be given as a matrix. So using paradigms like ...
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Solid Mechanics FEM Simulation with Different Material Properties
This is answer for the first question about titanium and nickel usage in one installation, and for the last question about how to speed up evaluation. First step is a mesh generation and visualization ...
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Solid Mechanics FEM Simulation with Different Material Properties
With the help of user21, the following code simulates the Eigenmodes of a solid component with two different densities and compliance matrices based on position within the mesh.
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Displaying NDEigensystem Results
Use VectorDisplacementPlot3D, however, the domain needs to reference the original geometric solid or boundary mesh region (the method I recommend ...
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NDEigensystem potential with a singularity
Since your potential is singular at the origin, an additional condition is needed: vanishing function at $x=0$. Replacing {x, -l, l} by {x, 0, l} with l=4 does the work.
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How can i know the number of times that an eigenvalue is degenerate for a large matrix?
If your memory is big enough to compute the orthogonal projector to the complement of each eigenvector and look for another eigenvalue of the same value in the projected matrix
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Optimal basis set of Gaussian functions for describing a quantum system (part 2)
In the paper "Hydrogen-Like Systems in Arbitrary Magnetic Fields. A Variational Approach" the method to optimize basis functions has been proposed. They described basis functions dependent ...
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Optimal basis set of Gaussian functions for describing a quantum system (part 1)
Maxwell: There are three forms of fields: |E|=|B| light, |E|>|B| electric fields with a bit of movement of charges. |E|<|B| magetic fields of strong neutral current or worse spin fields on ...
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Optimal basis set of Gaussian functions for describing a quantum system (part 1)
To compute exited states $\Psi_i$ with some basis functions $\Phi_j$ we need to solve equation
$H\Psi=\lambda U\Psi$, where $H_{ij}=\langle\Psi_i|\hat{H}|\Psi_j\rangle$, and $U_{ij}=\langle\Phi_i|\...
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Step by Step for Generalized Eigenvectors?
This is an update to make it handle geometric multiplicity>1.
When an eigenvalue has geometric multiplicity=1, then this will use the basic method of solving $(A-\lambda I) v_2 = v_1$ to find the ...
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Finding excited states using the condition of wave functions orthogonality
Following @Alex Trounev answer. Let's find the energy of the second excited state. Now it is necessary to take into account two conditions of orthogonality, since the second excited state is ...
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Finding excited states using the condition of wave functions orthogonality
To compute exited states we can use the penalty method as follows. Note that any exited state wave function is orthogonal to the ground state, therefore $\langle\Psi_1|\Psi_0\rangle=0$. We use this ...
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Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set?
We use code from our answer here. With a small modifications we have
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Why does the minimum eigenvalue change dramatically when one basis function is added to the basis set?
In the standard approach to find the spectrum of an operator
$\left\{ H=-\Delta_{r,r} + V\left(r \right), d\mu= r d r, r>0\right\}$
on the unit sphere in the Hilbert space
$\mathit H = \left\{ r \...
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How to expand the existing basis set so that it becomes more complete?
Its a pure mathematical question.
In cylindrical coordinates with an atractive plane 1/r Coulomb potential and and a harmonic oscillator in the x,y plane, in states with plane integer angular momentum ...
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Plot of the real part of the maximum eigenvalue of matrix
$Version
(* "13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023)" *)
Clear["Global`*"]
There should not be any patterns (e.g., ...
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Automatically obtain feature equations
Your equation has wrong syntax. x^\[Prime]\[Prime]) should be written like: x'' (not back ticks and no superscript). Then we can ...
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