Recent content by naffin

So the quantum mechanical description should be this one: if we start sending lots of photons at a time, the first of them will be detected with a probability of 50% on each detector because of the large difference in the two "possible paths", while the others will interfere among them producing...

In a first approximation we can ignore the quantity \vec{k} \cdot \vec{x} = \frac{2 \pi}{\lambda} \hat{k} \cdot \vec{x} because EM-induced atomic transitions involve radiation of length \approx 10^{3} angstroms, and the integral is essentially in a domain with a characteristic length of 1...

Question about the Mach-Zehnder interferometer experiment Let's consider a Mach–Zehnder interferometer with a significant difference in length between the two physical paths. The optical paths are set up such that the two beams interfere 100% destructively on one of the two detectors. What...

From Wikipedia - "Heisenberg picture" : "By the Stone-von Neumann theorem, the Heisenberg picture and the Schrödinger picture are unitarily equivalent." As far as I know that theorem proves the equivalence between Heisenberg matrix representation and Schrödinger wave representation, time...

All my divagation was essentially due to the evolution aspect of a system (the parameter b), which somehow separates the time translational symmetry from the others, while Francesco's argument was about treating space and time on equal footing. I don't know anything about black holes, but (for...

In my frame of reference I describe a particle with a function | \psi(t) \rangle . Let's focus on a precise time t_0 , for example when the particle changes its color; actually in quantum mechanics you see the color only by measurement, in this sense it is a 'classical' example: I'm not...

I've seen that conservation of transition probabilities is often interpreted as conservation of information or entropy. An interesting accessible paper for example is: http://arxiv.org/abs/quant-ph/0407118

Uhm, the operator U_{s}(t) that I am using is different than Weinberg's, and I was assuming |b \rangle as an arbitrary time-indipendent vector. Anyway I realize that using time-indipendent vectors in my previous example was obscuring the main idea, so I try to be more clear. In my reference...

The difference between space and time is that a system evolves with time, not with space. I think I've found a nice way to explain what I was trying to say: in a given frame of reference we describe a system with a trajectory in the space of states \psi(t) . It seems obvious to me that in any...

A transformation between states (rays) is implementable by a unitary operator if and only if it is one-to-one and preserves transitions probabilites. Let's focus on the Schrödinger picture: at a certain time t we describe a system configuration with a vector \psi . The obvious thing to say...

I think that Weinberg's derivation is misleading because he assumes a priori unitary evolution using the Heisenberg picture, in which states don't evolve in time, so the probability transitions are trivially constant. In the Schrödinger picture if we look at a system at time t in a...

Does someone have any proof ? I think we have to make other assumptions.

I'd like to know an example, too.

True, we know also that \left[ Q_{\alpha},P_{\beta} \right] = i \delta_{\alpha \beta} , but we don't know yet what is the group generated by Q (from a physical point of view). I've read App.4,5 and Ch.4, but without knowing the meaning of the group generated by Q I can't see how to...

Ballentine, pag. 89. For the exact solution I know "Quantum Mechanics I", Galindo-Pascual. In general they are just unitary operators, I don't know other structures.