Timeline for Understanding the Relationship Between the Principal Symbol of $-\Delta$ and $\sqrt{-\Delta}$ and Geodesic Flow in Hamiltonian Systems
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jun 19 at 8:42 | vote | accept | ayphyros | ||
| Jun 19 at 8:36 | comment | added | LPZ | I've added some details in the classical limit. If you're more interested in how to obtain the classical limit from the wave formulation, then you need to look into the general method of WKB/eikonal | |
| Jun 19 at 8:34 | history | edited | LPZ | CC BY-SA 4.0 |
added 654 characters in body
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| Jun 18 at 14:28 | comment | added | ayphyros | Thanks so much for the answer. I have a question when you afirm that you get the geodesic flow. Could you provide a reference where this is proved in a more formal way? In particular, I am working with quantum ergodic theory and there are references where it is stated that Time evolution is governed by $e^{-it\sqrt{-\Delta}}$ and sometimes is governed by $e^{-it{\Delta}}$. My aim is to use $-\Delta$ rather than the other. I am following PDE II Vol. of M. Taylor. | |
| Jun 18 at 14:21 | history | answered | LPZ | CC BY-SA 4.0 |