Timeline for Evolution of quantum state that cannot exist with accompanying Hamiltonian
Current License: CC BY-SA 4.0
5 events
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| Mar 24, 2020 at 13:32 | comment | added | CFRedDemon | I wonder if there's a way to get them out of the Hilbert space then? Or it probably is just wrong to start off with a certain state then, because it is physically impossible? Then again, if you have this Hamiltonian in real life it would not be hard to set up your system in a forbidden state as a free system and then "turn on" this Hamiltonian. This then just freezes the dynamics of the forbidden states. Interesting stuff. Also thanks for the remark on the 'So', I will remember that for when I write my thesis later this year. | |
| Mar 24, 2020 at 13:06 | comment | added | mike stone | @CFRedDemon. Ah! thanks for the remark about "So". I see it a lot and wondered where it came from. It's not a good idea to use it in formal english. It looks odd, but does not affect the understandablity. I also see what you mean about "forbidden" The states are still in the Hilbert space, but they are isolated from all others. They must not be killed by time evolution however, or that would lose the state normalization. | |
| Mar 24, 2020 at 12:52 | comment | added | CFRedDemon | As for the starting with the "So", I'm not a native speaker and I tend to do that a lot, because it's common in my language to start off with that same word ;) | |
| Mar 24, 2020 at 12:52 | comment | added | CFRedDemon | Well in my specific case the projection operator is meant to project out these states because they cannot exist. I am actually looking at a many-body problem here and it's an array of spin sites, in which neighboring spins cannot be both in the excited state (Rydberg blockade). I just find it strange that if would start with a state that has certain overlaps with these "forbidden" states, they remain in this state forever as they are not projected out in time evolution or anything. They just remain "static" as E=0 indeed. | |
| Mar 24, 2020 at 12:46 | history | answered | mike stone | CC BY-SA 4.0 |