Timeline for "Complete" confusion
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2015 at 21:17 | comment | added | gilonik | My apologies if I sounded combative -- I'm trying to understand the terminology, not fight over it! But I think you (and yuugib) hit the key distinction: completeness is a metric space concept, and so is not as "primitive" as a basis or spanning set. | |
| Jun 3, 2015 at 21:07 | comment | added | Timaeus | @gilonik The word complete does require a metric (so an inner product would do). When you say something is overcomplete you mean that you can remove things from it and have it still be complete. The same things happen with spanning sets, you might want to add more vectors to get a frame that is spanning and then some maybe for redundancy. Sometimes you like redundancy, sometimes you like unique linear combinations sometimes you like unique finite linear combinations. Set up your system to give you want you want, I'm trying to make you aware of the options not fight about terminology. | |
| Jun 3, 2015 at 20:15 | comment | added | gilonik | An overcomplete set is a spanning set. But it still seems to me that (over)complete in the QM sense requires an inner product space | |
| Jun 3, 2015 at 19:24 | comment | added | gilonik | They would be complete -- but then they'd be neither orthogonal nor normalized! | |
| Jun 3, 2015 at 19:17 | comment | added | aquirdturtle | Could you not just add a factor of 1/sqrt(pi) to one of the states? the states would then be complete, and still not orthogonal? | |
| Jun 3, 2015 at 19:15 | comment | added | zeldredge | Ah. The integral over all the coherent states is $\pi I$. I'll think about your actual question, then, maybe I'll come up with a weird degenerate case (or a counterproof). | |
| Jun 3, 2015 at 19:11 | comment | added | gilonik | By complete in the "QM sense" I mean the sum/integral over ket-bra being unity. | |
| Jun 3, 2015 at 19:02 | history | answered | zeldredge | CC BY-SA 3.0 |