Timeline for Sorting eigenvalues by the dominant contribution
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 13, 2018 at 12:19 | vote | accept | boyfarrell | ||
| Nov 12, 2018 at 21:47 | answer | added | deemaregee | timeline score: 4 | |
| Feb 5, 2014 at 16:04 | comment | added | Bill Barth | What do the eigenvectors associated with the largest (in magnitude) eigenvalues look like? Do those give you the "bands". I'm not a semiconductor person, so I'm not sure what a band is. | |
| Feb 5, 2014 at 15:25 | comment | added | boyfarrell | Thanks for the comments. I interpret this to mean that the wavefunctions by the very nature are mixed in character (they have components from all 8 bands), so there is not a unique band. I'm trying to get a method that associates the eigenvalues to the physical bands by the dominant contribution. For each band I have been using the largest $|\Psi_j|^2$ in each row (where $j$ is the row index) maybe that method is floored? Maybe there is another way to associate the eigenvalues with a band? Any clever ideas? | |
| Feb 5, 2014 at 14:35 | comment | added | Bill Barth | I don't think it works that way. The eigen-decomposition for your presumably Hermitian matrix gives you a basis for $\mathbb{C}^n$ in which you can represent your right-hand side and solution. Each eigenvalue can only really be said to attribute anything to its associated eigenvector(s). That being said, you should be able to look at the eigenvectors associated with the eigenvalues that interest you and say something about which physical bands they are associated with. | |
| Feb 5, 2014 at 12:50 | history | edited | boyfarrell | CC BY-SA 3.0 |
Re-introduced physics.
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| Feb 5, 2014 at 12:38 | comment | added | boyfarrell | Well actually physics. I had written a more physics type question (an earlier version) which explain the background. Basically I am solving a k.p hamiltonian and I want to be able to attribute its eigenvalues (the semiconductor bands) to a particular row in the Hamiltonian, where the row indicated how I should interpret the eigenvalue; i.e. it's a conduction band, valence band etc. Maybe I can reinstate some of the physics. | |
| Feb 5, 2014 at 11:50 | comment | added | Bill Barth | What's the goal here? | |
| Feb 5, 2014 at 10:12 | history | edited | boyfarrell | CC BY-SA 3.0 |
Simplification because no views.
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| Feb 5, 2014 at 8:41 | history | edited | boyfarrell | CC BY-SA 3.0 |
added 20 characters in body
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| Feb 5, 2014 at 8:29 | history | asked | boyfarrell | CC BY-SA 3.0 |