Timeline for Perturbation of first eigenvalue
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2022 at 23:14 | comment | added | Math604 | thank you very much for your answer. I ended up writing it out term by term and solving...but i wanted to do some abstract thing to get the remainder term $ \psi_\epsilon$ and $ \lambda^\epsilon$; which I managed to do today. My mistake was that I wasn't treating $ \lambda^\epsilon$ as 'free'. I can attempt to write out some details of what I did. thanks for your comments; they helped. | |
| May 20, 2022 at 13:47 | comment | added | Michael Engelhardt | Just to add the usual expression for $\phi_{\epsilon } $, since it may be useful: $\phi_{\epsilon } = \phi_{0} + \epsilon \sum_{k\neq 0} \frac{\langle \phi_{k} | \gamma | \phi_{0} \rangle }{\lambda_{0} - \lambda_{k} } \phi_{k} + \ldots $ where $(\lambda_{k} ,\phi_{k} )$ are all the other unperturbed solutions. | |
| May 20, 2022 at 4:13 | comment | added | Math604 | I assume the usual perturbation theory expressions are satisfactory (but I don't know them hence...). I do realize I didn't write out the equation for $ \psi_\epsilon$ and hence its not at all clear what I even asking. I will add the rest to make a very specific queststion. | |
| May 20, 2022 at 3:58 | comment | added | Michael Engelhardt | I have trouble understanding what the question is aiming at. Why are the usual perturbation theory expressions unsatisfactory, i.e., $\lambda_{\epsilon } = \lambda_{0} + \epsilon \langle \phi_{0} | \gamma | \phi_{0} \rangle + \ldots $, etc. | |
| May 20, 2022 at 2:00 | history | asked | Math604 | CC BY-SA 4.0 |