Ondřej Černotík
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 May 28 comment In terms of covariance matrices, are partial measurement and partial trace equivalent? @JessRiedel There are some excellent papers on the topic of general completely positive transformations of Gaussian states, see, e.g., this one or this one. Hope that helps! May 25 comment Is there an inconsistency between Quantum and Classic in probability density of harmonic oscillator ground state? The problem with ground state (both quantum and classical) is that it is the state with minimum energy. In the classical regime that means no oscillation and, therefore, position at the equillibrium. The quantum ground state then represents smearing of this equilibrium and one has to look at excited quantum states if one wants to compare that to classical oscillations. May 21 comment Quantum entropy in term of density matrix It is not entirely true that the off-diagonal terms don't play a role - there is the logarithm of the density matrix which is not given just by the diagonal terms - either you need to diagonalize the density matrix before taking the logarithm, or you express the logarithm by its Taylor expansion. And then, the off-diagonal terms come into play. Dec 29 comment Is it possible to “cook” pasta at room temperature with low enough pressure? That is also why pressure cooking is used. If you cook something at higher pressure, the water will boil at higher temperature. You then cook at higher temperature and the cooking process is faster. Nov 22 comment Orthogonality between $\vec{E}$ and $\vec{H}$ waves with space-dependent amplitudes $\vec{S}$ is certainly orthogonal to both $\vec{E}$, $\vec{H}$ because it is defined as their vector product. But the orthogonality of $\vec{E}$ and $\vec{H}$ is far less trivial. I can't see any simple proof now but I believe that one can show their orthogonality. May 27 comment QM the superposition principle +1 However, you forgot to include time in the exponential. Also note that you can include the time evolution $\exp(-iE_it/\hbar)$ in the coefficients in the expansion which is something I'm used to seeing more often. May 26 comment Find E and B from vector potential @DenverDang Exactly :) May 26 comment Help me check units Since when is density volume per mass?? As far as I know, it's always been the other way around. If you express pascal using force per area, you get $\mathrm{kg}\cdot\mathrm{m}^{-1}\cdot\mathrm{s}^{-2}$. May 25 comment Why do prisms work (why is refraction frequency dependent)? @BenCrowell It certainly is an unusual explanation for dispersion but I guess it could still work. You'd just need to do the calculations in detail to check it. And there is one more thing - it explains dispersion only in crystals, not in, e.g., glass. May 25 comment Why do prisms work (why is refraction frequency dependent)? @fffred Yes, $k$ comes from the dipole oscillations of the electron. I thought that the basic meaning was clear from the text and I don't want to go into much detail concerning finding specific values of the constants. I am certain one can find more details in the literature; this is just to give the main idea. May 24 comment Zero point fluctuation of an harmonic oscillator You could also argue that when defining zero point fluctuations in terms of variance of the position, the value will be smaller than the amplitude. I bet you would find that the variance (or its square root) will be exactly $\sqrt{2}$ times smaller. May 23 comment Magnitude of a photon? @annav I know that. What I mean is that they probably mean splitting its probability amplitude among several modes. It's not the same thing and the term "splitting a photon" is definitely not a suitable one, but this is where I think the core of the statement might be. May 23 comment Magnitude of a photon? Maybe they mean that they send the photon on a beam splitter (or a set of them) so that, technically, the photon is "split" into all the output modes. The formulation is not ideal but that might also depend on the context in which the whole formulation is used. May 22 comment Quantum mechanics and everyday nature @joshphysics I agree with you that once you accept that light beam is made of particles, you need quantum physics to explain Young's experiment. But the problem here is the acceptance bit. If you try and explain this to someone who knows nothing about quantum physics, they'll ask why you assume light is made of particles and how they can see it. So you get nowhere and still need a convincing everyday phenomenon that illustrates the importance of quantum physics. May 22 comment Quantum mechanics and everyday nature Sure, you can explain Young's experiment with macroscopic light intensities using quantum physics. But the question asks for phenomena that can be explained only using quantum mechanics. Therefore you need single photons interfering to have the need to turn to quantum mechanics. Otherwise, you do not even need Maxwell's equations and are perfectly happy with a wave-optical explanation. May 21 comment Quantum mechanics and everyday nature Young's experiment actually just demonstrates wave nature of light. If you wanted to show its quantumness, you would need to show wave-particle duality using single photon sources and single photon detectors which I doubt people usually have lying around. May 11 comment Reflection of a polarised beam I think that if you used a linearly polarizing filter, you could have a situation in which all light is transmitted through the beam splitter, reflecting no light on the AF sensor. When there is no light on the sensor, the system cannot, of course, focus the lens. May 11 comment Reflection of a polarised beam That depends on the precise polarization state. If the light is polarized linearly but in a combination of parallel and perpendicular orientations with respect to the boundary then you need to apply Fresnel equations for each of the components and combine them again after the interaction. So the state can indeed be affected. May 11 comment Reflection of a polarised beam Ever heard of Fresnel equations? May 8 comment Coherent State, Unitary Operators, Harmonic Oscillator I'll get to it in a while, having a busy week. Please be patient.