I guess we are talking about nonrelativistic QM, not about QFT. If you have two particles, each moving in 3 dimensions, you can think of it as one particle in 6 dimensions. Write the path integral by pretending it's one particle in 6 dimensions, and you will get the right result.
The observables such as energy, momentum, angular momentum and charge are conserved in the sense that the corresponding operator does not have an explicit time dependence. Let ##A## be any observable conserved in that sense. If you measure A (and hence collapse the state) and then measure A...
Right, but decoherence cannot be properly understood without its derivation. You can describe decoherence by phenomenological models without explicitly taking into account the environment, but such models lack deep understanding.
I solve PDE's for work quite often. But I'm a professional scientist, so I guess it doesn't count. :D
What do people with math or physics major do if they do not become scientists? I guess most of them become programmers of a kind, so maybe solving PDE's is not something what most of them do.
That's a big problem in most fundamental research nowadays. The goal of fundamental research should be the increase in understanding, not the increase in the number of published papers. Unfortunately, this is often not the case. Sorry for the off topic!
Eisberg Resnick
https://www.amazon.com/Quantum-Physics-Molecules-Solids-Particles/dp/047187373X?tag=pfamazon01-20
puts more emphasis on concepts than on formalism.