>>13779136I think this point is incredibly important so I'll reiterate it.
What are the energy levels of hydrogen?
E=-13.6eV/n^2
ok. fine. this can be measured and no one disagrees.
lets think about Schrodinger's equations now. We'll find the radial solution to the hydrogen nucleus potential is not the energy levels of the hydrogen atom. What will we find? We'll find the EIGEN VALUES of the differential equation are 1/n^2. Oh, but the eigen values are the solutions, right? NO. FUCK NO. the solution to Schrodinger's equation is any LINEAR COMBINATION of EIGEN VALUES. so a solution to schrodingers equation looks like a0/n0^2+a1/n1^2+a2/n2^2+a3/n3^2. So if you naively solve shcrodingers equation you DON'T get a QUANTUM solution.
The work around is the critical process in QM. It's called wave function collapse. You can claim it's a physical process and the Schrodinger's equation is a physical equation, or you can wave your arms and say it's just a statistics equation and the Schrodinger's equation does not describe a physical process, but to get the right QUANTUM solution you NEED wave function collapse, regardless.
The rule of wave function collapse is that "the value you measure upon observation" is an EIGEN VALUE of the Schrodinger equation, so using this rule the other linearly independent solutions vanish and you are just left with one eigenfunction and value which is E=-13.6eV.
so what would you observe without wave function collapse? just a linear combination of a random assortment of a0/n0^2+a1/n1^2+a2/n2^2+a3/n3^2, so literally a continuous spectrum. you ABSOLUTELY NEED wave function collapse to get you something QUANTUM.
My take is an intelligent person will interpret this just as a math trick that gets you the right answer from a fitted statistical model, and interpreting Schrodinger's equation as a physical process is misguided.
you could think Schrodinger's equation is a physical equation, and wave function is physical.
