Recent content by Coelum

Our thesis can be restated as follows: \exists C_\alpha\in\mathbb R_+ s.t. \forall w\in\mathbb R^2_+ \begin{align*} \lVert u(t,w)-u(t,w')\rVert^2 \leq C_\alpha^2\lVert w-w'\rVert^{2\alpha} \end{align*} where w=(y,z) and \alpha=\beta\gamma. We get an upper bound for each (squared) component of...

Great reference, thanks!

First of all, I want to thank all the kind people who took the time to try and help me understand better. I'm aware I am touching a critical point. To make things worst, I was not able to present my thoughts in a clean, ordered way... As next step, I will read the paper quoted by @romsofia...

1- what is the meaning of measurement? how is it different from any other interaction? 2- how can we derive irreversible laws from reversible laws without additional assumptions? 3- maybe - I'm here to learn.

I am having a hard time presenting my concerns about the measurement process. So, let me try a different point of view. How can it be that the Universe behaves differently when a human being observes (i.e., measures)? We can try and save the measurement postulate (von Neumann projection...

I have no issue with the interpretation. I suspect that the measurement process is not correctly modelled. After all, the measurement process is irreversible, while QM is not. Are you aware of any analysis along this line of thought?

OK, how can I move it?

I agree, my point is: is energy conserved for the closed system made up of the quantum system and the observer? Quoting Sean Carroll: "One purpose of this paper is to show that this is not the case, and that the total energy of the system plus apparatus plus environment can change."

Dear PFer's, this is a problem I have been struggling with for years. Is energy conserved (not in a statistical sense) in QM? The so-called collapse of the wavefunction, occurring during a measurement process, is incompatible with energy conservation - at least in the general case. A starting...

Yes, I got it. Using PeroK's notation, it is ##\alpha=-i##. In fact, one of the two conditions 1 and 2 is redundant. I got the solution using conditions 1 and 3 only. It automatically checks condition 2. Thanks everybody for your help!

In fact, I did not normalize the eigenvectors, just the state. I cannot see any further simplification of ##\Psi_0## beyond what I already did. I cannot replicate your results. I'm still stuck with the two nonlinear equations for the three phases ##\phi_a## and ##\phi_b## from the first two...

@PeroK: thanks a lot for your remarks. Let me fix my errors: You pointed out one error: I cannot take an arbitrary phase for the expression of ##\Psi_0## in terms of the eigenvectors of ##B## since I already took that liberty. I found another (minor) error: I forgot the ##a## and ##b## factors...

TL;DR Summary: Find the initial state of a two-level quantum system, given the probability of measurements for two observables and the expected value of an operator. Dear PFer's, I have been struggling with the following problem. It was assigned at an exam last year. Problem Statement For a...

When Einstein explained the Brownian motion in one of his wonderful papers of 1905 (https://www.maths.usyd.edu.au/u/UG/SM/MATH3075/r/Einstein_1905.pdf), he used classical mechanics only. Quantum mechanics was not invented yet, though Einstein himself was concurrently working on it. Unless you...

Yes, it looks to me like a mix of bound and unbound states. On one hand, the classical corresponding state is bound. On the other hand, it is not normalizable, so it should represent a stream of particles. Also, there is a well-defined condition for it to exist. Not all wells allow such a state...