Anonymous at Fri, 24 Jan 2025 22:38:36 UTC No. 16562922

>>16562822
Wow, bases on Hilbert spaces follow the completeness relation! It's not like they tautologically do because Hilbert spaces are complete by definition...

Anonymous at Sat, 25 Jan 2025 00:34:40 UTC No. 16563026

>>16562822
Dirac notation is a crime against humanity.

Anonymous at Sat, 25 Jan 2025 00:38:44 UTC No. 16563030

>>16563026
Explain why without appealing to
>uhhhhh I'm just used to a different notation
It neatly captures the notions of the dual vector space and the norm. It starts failing in two cases: anti-linear operators and tensor contractions. But anti-linear operators are never touched in QM because the only one I'm aware of, time-inversion, can be replaced with CP. And by the time you're working with tensors, you're likely doing advanced enough QFT stuff that you'll be using the Einstein index notation anyways.

Anonymous at Sat, 25 Jan 2025 12:21:15 UTC No. 16563400

>>16562822
what do you think, does this formula work for anything we denote by 'x', or only for spectral projectors?