I think both questions are informative, they just test a different thing.
To give an analogy from copmputer science, the question about hydrogen atom is similar in spirit to, “Would you be able to implement quicksort?”, whereas the one about Bell theorem is more like, “Would you be able to reconstruct the halting problem proof?” The latter seems like a much higher bar. I’m curious, do you think there exist many people who can actually reconstruct the proof of Bell’s theorem, but who can’t solve the Schrodinger equation for the hydrogen atom?
(I’m assuming that by solving the Schrodinger equation for the hydrogen atom, Daniel meant deriving the energy levels of a hydrogen atom from SE, as opposed to say providing the full basis of eigenfunctions including these for E > 0; the latter is much harder and I wouldn’t expect most people who took even advanced Quantum Mechanics to be able to do it without looking things up).
I’m assuming that by solving the Schrodinger equation for the hydrogen atom, Daniel meant deriving the energy levels of a hydrogen atom from SE, as opposed to say providing the full basis of eigenfunctions including these for E > 0;
I had assumed something in between—deriving the energy levels, and the eigenfunctions for the levels with E < 0.
Maybe the answers given (either in the Bell theorem case or in the Schrödinger equation case) could be “Yes, right now”, “Not off the top of my head, but I know where to look stuff up” and “Can I prove the what?”
I think both questions are informative, they just test a different thing.
To give an analogy from copmputer science, the question about hydrogen atom is similar in spirit to, “Would you be able to implement quicksort?”, whereas the one about Bell theorem is more like, “Would you be able to reconstruct the halting problem proof?” The latter seems like a much higher bar. I’m curious, do you think there exist many people who can actually reconstruct the proof of Bell’s theorem, but who can’t solve the Schrodinger equation for the hydrogen atom?
(I’m assuming that by solving the Schrodinger equation for the hydrogen atom, Daniel meant deriving the energy levels of a hydrogen atom from SE, as opposed to say providing the full basis of eigenfunctions including these for E > 0; the latter is much harder and I wouldn’t expect most people who took even advanced Quantum Mechanics to be able to do it without looking things up).
I had assumed something in between—deriving the energy levels, and the eigenfunctions for the levels with E < 0.
Maybe the answers given (either in the Bell theorem case or in the Schrödinger equation case) could be “Yes, right now”, “Not off the top of my head, but I know where to look stuff up” and “Can I prove the what?”