@SillyGoose definitely

@qwerty the "gets brighter" has nothing quantum to it. He is absolutely correct. There is nothing weird about it from a classical waves perspective. All the weirdness comes from when you realise that you must have an explanation for how photons go through them one by one.

@Feynmate miao miao rarely deals merely with memes...

Is there a reason why sometimes in order to solve the K.G equation we consider $\Phi(x^\mu)=e^{-ix_\mup^\mu}$ and sometimes a fourier transform of it $\phi(x)=\int \frac{1}{(2\pi)^3}e^{i\vec p \vec x}\tilde{\Phi(t,\vec p)}d^3p$ ?

@User198 You are so close that Tobias did not even want to stress the small difference. You have a weighted sum with classical probabilities, so the equations must be $$\begin{align}\tag1\rho(t)&=\sum_jp_j\left|\psi_j(t)\right>\!\left<\psi_j(t)\right|\\\tag2&=\sum_jp_jU(t-t_0)\left|\psi_j(t_0)\right>\!\left<\psi_j(t_0)\right|U^\dagger(t,t_0)\\\tag3&=U(t,t_0)\left(\sum_jp_j\left|\psi_j(t_0)\right>\!\left<\psi_j(t_0)\right|\right)U^\dagger(t-t_0)\end {align}$$

Hence, if you postulated quantum dynamics for wavefunctions, then you will automatically obtain the correct dynamics for density operators by this derivation.

another misleading statement: "the partition function for a system of non-interacting particles factors"

someone needs to take you to fock space...

@SillyGoose who says that and where?

I've pointed out, again in a link I had posted here, that this is in general only true for the GCE, and the factorization is with respect to the single-particle states.

I really do not know where you got all the statements from ^^. I cannot remember reading such a single isolated statement in any book.

to add: what I refer to was for indistinguishable particles. for distinguishable ones it is indeed much easier, and can be generalized, I think.

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> While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved... While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted theoretical physics research may become possible in the near future.

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Why do so many people here have problems in accepting answers? For example, I know like 2-4 users who constantly fail to accept (very good) answers, for the vast majority of their questions (and they have many many, and even like around 10k rep).

I am then trying to point this out, and sometimes it works and sometimes not. I don't consider this fair, given how the site is intended to work. No?

I don't know about the cases you're talking about, but it's possible that the OP might not understand the answer(s) fully and therefore delay or then forget endorsing them