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Yvain comments on 2012 Survey Results - Less Wrong
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The actual survey specified "can solve the Schrodinger equation for a hydrogen atom". Although it is not exactly synonymous with "understands quantum mechanics", you would expect them to be highly correlated.
Right, sorry, I forgot that qualifier since the time I took the survey. It does imply more familiarity with the underlying math than the simplest possible cases. Still, I recall that when I was at that level, I was untroubled by the foundational issues, just being happy to have mastered the math.
I wonder if there is a way to test this assertion. One would presumably start by defining what "understands quantum mechanics" means.
When I was learning to solve the hydrogen atom, they didn't even talk about the foundational issues, just waved it off with some wave-particle duality nonsense. But still, it seems like as good a criterion as you're going to get, unless you want to ask if people have a Master in Physics (Quantum).
I suppose that a better question would be related to the EPR paradox, but I'm not sure what academic course would cover it.