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 Oct 16 answered Proof of quantum mechanical position uncertainty Oct 16 comment Proof of quantum mechanical position uncertainty I'm afraid your step is incorrect (the last formula). Expanding $\langle(x-\langle x \rangle)^2\rangle$ you obtain $\langle x^2 -2x \langle x \rangle x - \langle x \rangle^2\rangle$. From here you only need to use that $\langle x \rangle$ is a number and that expectation value is linear. Since this looks like a homework, I won't work it all out for you (important part of the learning process in physics is to calculate things for yourself). But hopefully this is enough of a hint to get you to the right answer. Oct 15 comment Mathematically challenging areas in Quantum information theory and quantum cryptography If you are into more mathematically challenging things, you could start here: arxiv.org/abs/1106.1445. A review article titled "From classical to quantum shannon theory" mostly skips through the linear algebra and goes straight to the rigorous quantum info. Recommended. You might also want to know that entanglement is nowadays seen more as only one of the resources and that other resources such as quantum discord are gaining in importance. Oct 14 comment Is there still light in practical darkness? Do photons penetrate everywhere? Right, I agree. Oct 13 comment Is there still light in practical darkness? Do photons penetrate everywhere? Yes, and with the typical temperatures they would radiate at infrared wavelengths, not something you can typically see unless the object is very hot (hence the red glow of very hot objects). Oct 12 awarded Critic Oct 12 reviewed Reviewed Why do we use Hermitian operators in QM? Oct 12 comment What is the physical size of a black hole? Yes, I know that. But in the frame of an asymptotic observer that happens only as $t \rightarrow \infty$. See also a related question: physics.stackexchange.com/questions/21319/… Oct 11 comment decoherence free subspace of a single photon Do you know the Kraus operators of the second order polarization mode dispersion when you take frequency as a classical variable? Oct 11 comment decoherence free subspace of a single photon Basically what you are looking at is to find whether there are entangled states in this family that are fixed points of the decoherence operator (or at least nearly so). To know what will happen you therefore need to know what decoherence operator you expect to act here. Oct 11 awarded Custodian Oct 11 reviewed Reviewed Getting started self-studying general relativity Oct 11 reviewed Reviewed Can you use a wormhole to travel through space not time? Oct 11 reviewed Reviewed Negative probabilities in quantum physics Oct 11 reviewed Reviewed Books to study quantum thermodynamics and quantum decoherence Oct 11 reviewed Reviewed Can a single particle create a black hole? Oct 11 reviewed Reviewed Hamiltonian of oscillators quantized proof Oct 11 reviewed Reviewed Show that the Hamiltonian operator commutes with the angular momentum operator Oct 11 reviewed Reviewed Study Quantum Physics Oct 11 reviewed Reviewed When do the von Neumann projections occur and what causes them?