Quantum Definition and 999 Threads

https://www.guardianmag.us/2023/02/scientists-levitate-glass-nanosphere.html "the nanosphere was suspended in its lowest quantum mechanical state, one of extremely limited motion where quantum behavior can start to happen." To my reading, the glass bead was cooled down and then suspended with...

The lowest two energy level corrections (l=0, s_{z}=-1/2 and l=0, s_{z}=1/2) are easy to work out since the eigenvalues are not degenerate and the unperturbed energy levels also happen to be eigenstates of H'. However I have three degenerate energy levels for the third eigenvalue of the form...

Hi guys, I have a problem with point 2 of this exercise: The electron of a hydrogen atom is initially found in the state: having considered the quantum numbers n,l,m and epsilon related to the operators H, L^2, Lz and Sz. I am asked: determine the possible outcomes of a measurement of J^2...

Next, we assume a solution in this form: Which simplifies (according to my notes) to this: In the middle equation, we have factorised out the F(t). My question is why is it wavefunction(x,t) rather than wavefunction(x). I first thought it was a mistake in the notes, but it uses the same...

In reading Weinberg volume 1 I learned gravity is not renormalizable by Dyson power counting. This means that it has an infinite number of free parameters, and such theories lose their predictive power at energies of the common mass scale. This being said, T Hooft and Veltman showed miraculously...

Many more questions....please enlighten me on this topic. thank you!

I was tryingt to find away to build a setup for conducting the quantum erase experiment, demonstrating the observer effect. It seemed impossible without expensive equipment for sending single photont and detecting single photons, then however I bumbed into this guide from scientific american...

Well, I am not making any exciting claims or anything, just asking a question that I cannot stop asking myself. WE all know the Quantum theory on spontaneous generation of particles in a vacuum etc and many have asked is this linked to dark energy somehow. I like to try Einstein type Thought...

Hi, when normalising the wavefunction I get two answers. Is this correct? My notes only has 1/sqrt(L) = A.

TL;DR Summary: Why is HgCl2 more covalent than CaCl2 via shielding? Hg^2+ in HgCl_2 has more shells of p-orbitals and s-orbitals than Ca^2+ in CaCl2 - Do those extra p and s shells of Hg^2 in HgCl2 shield the two chlorines in HgCl2 from the effect of Hg^2+'s nucleus attraction, or leave the...

If we have a pair of super-asymmetrical entwined particles, and move them a light year away so that they retain their quantum entanglement, and we set a clockwise spin as 0 and a counter-clockwise spin as 1. Would it be possible to transmit binary data faster than the speed of light? If we hold...

Sakurai's Modern Quantum Mechanics is 1/2 of a very good graduate textbook. Unfortunately Sakurai passed away midway through writing it, and it is very obvious exactly where it swapped from their writing to just using their notes. The back half of the book, while by no means bad, is notably less...

Student of master of physics.

A.E. Allahverdyan, R. Balian, and T.M. Nieuwenhuizen, Teaching ideal quantum measurement, from dynamics to interpretation, Comptes Rendus Physique 25 (2024), 251--287. https://www.researchgate.net/publication/380862732

If gravity is not a force, but rather curvature of spacetime, are gravitons necessary to couple with gravitational field?

I suppose, anybody here knows about the Elitzur–Vaidman bomb tester and the counterfactual definiteness: https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester https://en.wikipedia.org/wiki/Counterfactual_definiteness I have a question: can this experiment be performed at the level of...

Color charge is not scalar. Still, do their components have dimensions (in metrological terms)?

Firstly I have found the eigenstates for both the original well and the new well as the following $$\psi_{n,\frac{L}{2}} = \begin{cases} \sqrt{\frac{2}{L}} \cos{\frac{n \pi x}{L}} \; \; \; \; \; n \text{ odd} \\ \sqrt{\frac{2}{L}} \sin{\frac{n \pi x}{L}} \; \; \; \; \; n \text{ even}...

Am reading a book (Ballentine, "Quantum Mechanics: A modern development) which I have found very helpful. Am now puzzled by section 3.4, where the position operator satisfies Q|x> = x |x> (I have simplified from 3 dims to 1 dim). Here, x is any real number. There are, thus, uncountably many...

A physicist (I'm not a physicist by profession, as you'll have gathered) told me, without being more specific, that interference is not an 'interaction' in the strict sense of the word, in other words in the physical sense of the term. I can only guess at what is meant by this (but perhaps...

Every once in a while I use my ancient trick of searching something in google with keywords, and found the above article. I don't think there's a free copy of it, because it's from 1989. I guess I need to read the pink book on foundations of Q-Groups by Majid. You know who also has written a...

Hi everyone I'm Justina. I'm excited in joining physics forums and I'm high school student who is interested in Quantum mechanics a lot .I used to spend lot of time on knowing Quantum mechanics and i learnt few little things. And this is my first time, joining an online community hope I will...

I am a long-retired physics lecturer, with the bulk of my lecturing focused on quantum and relativity. I am still active in research. I have completely lost contact with the challenge of explaining this stuff to students, and was curious to see how these challenges are met on this forum, not...

I know this wavefunction should behave as a symmetric cosine function (possibly as Cos( (k∗x)/(hbar) ?). I also know for a bound state, the wavefunction must decay exponentially outside the well. Additionally, r = (-β+ik)/(β−ik) . However, aside from that, I do not know how to get this question...

IIUC, entanglement sometimes plays a role in conserving come quantity like momentum or spin: the quantities measured for two particles must be correlated in order to get a certain total value. But is this always the case? For example, what, if anything, is conserved in the Hong-Ou-Mandel...

In the 1934 novel by John Taine, Before the Dawn, scientists are able to retrieve images of the past by accessing the light absorbed by stones throughout history. While this is fictional, 1934 was really before the dawn of quantum physics. In the far future, could we retrieve images from light...

2 recent gains on loop quantum gravity theory arXiv:2403.18606 (gr-qc) [Submitted on 27 Mar 2024] Test the Loop Quantum Gravity Theory via the Lensing Effect Lai Zhao, Meirong Tang, Zhaoyi Xu https://doi.org/10.48550/arXiv.2403.18606 and [Submitted on 7 Dec 2023 (v1), last revised 28 Dec...

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shouldn't it be a sort of partially GR and partially QM? I mean in a sort of superposition of both theories such that in the specific limit becomes GR and another limit QM, and in the between both regions it's something entirely else, not QM and not GR. Is this possible? I haven't yet done the...

Hello I am MOHD HANZALA I worked on bell's inequality where we measure spin of electron along different basis leading to the bell's inequality . My question is that can we prove bell's inequality through proton or neutron or other particle??

How do quantum fluctuations affect the formation and evolution of structures in the universe on large scales?

I have read that if one measures the Hamiltonian and receives a value of h2, then the quantum state will be in ##|h2\rangle##. Finding the probability of a1 is done by projecting ##|a1\rangle## upon ##|h2\rangle## divided by ##\langle h2|h2\rangle##. In other words: $$\frac{|\langle...

Here we have four electron detectors (e.g. electron multipliers) forming positively charged detection regions, with a negative back plate. Mathematically, is it valid to describe this as a measurement with four eigenstates, considering that there are only four possible detection outcomes...

Hello! I am curious about how different rotations on the Bloch sphere are done in practice. For example, assuming we start in the lower energy state of the z-axis (call it |0>), a resonant rotation on the Bloch sphere by ##\pi/2## around the x-axis will take you to ##\frac{|0>-i|1>}{\sqrt{2}}##...

I can write $$\psi(x,t_0) =\frac{1}{\sqrt{2}}(e^{\frac{-iE_1}{\hbar}t_0}\psi_1(x) +e^{\frac{-iE_2}{\hbar}t_0}\psi_2(x))$$ for the second coefficient to be -1 i need ## -1=e^{-i\pi}=e^{\frac{-iE_2}{\hbar}t_0} ## so ##t_0=\frac{\pi\hbar}{E_2}## and the above equation becomes $$\psi(x,t_0)...

Sorry to open a new thread. There are plenty of threads on PF dealing with the issue of "wave-particle duality". Although not unanimously, many agree that the concept of "wave-particle duality" is outdated. Electrons, photons and all of the underlying entities are neither waves nor particles...

I have already solved question number 1 by applying the schrödinger equation obtaining that $$\ket{\psi_2}(t) = \cos(\Omega t)\ket{g} - i \sin (\Omega t)\ket{s}$$ and therefore in ##t=\frac{\pi}{4\Omega}## $$\ket{\psi_2}(t) = \dfrac{1}{\sqrt{2}}(\ket{g} - i \ket{s})$$ I have some doubts...

Consider the state ##\ket{\Psi} = \sum_{1 \leq n_{1} \leq n_{2} \leq N} a(n_{1},n_{2})\ket{n_{1},n_{2}}## and suppose $$|a(n_{1},n_{2})| \propto \cosh[(x-1/2)N\ln N]$$ where ##0<x=(n_{1}-n_{2})/N<1##. The claim is that all ##a(n_{1},n_{2})## with ##n_{2}-n_{1} > 1## go to ##0## as...

TL;DR Summary: Looking for help on a Intro to QM Problem Hi All, THIS IS A GRADED PIECE OF WORK AT MY UNIVERSITY PLEASE DO NOT JUST GIVE ME THE ANSWER , I have made this post to see if what i've calculated seems reasonable, it sounds unlikely as 0.4 - 0.5L is in the middle of the well. The...

https://www.science.org/doi/10.1126/sciadv.adk2949

Google is looking for practical problems/algorithms that can be solved on quantum computers: https://www.xprize.org/prizes/qc-apps

This is the statement in question: But if they were scalar fields, they would not transform at all. How could they contribute differently if they didn't change?

This is technically a Fourier transform of a quantum function, but the problem I'm having is solely mathematical. Conducting this integral is relatively straightforward. We can pull the square roots out since they are constants, rewrite the bounds of the integral to be from ##-a## to ##a##...

Hello, I have a few questions about these images that I shared. 1) What does t represent? I am assuming Es is the energy of the atoms before they hybridize, and that t is either the gain or reduction of energy due to the new orbitals that are formed through bonding. Am I way off on this? 2)...

Anyone read these books and care to share their thoughts? https://www.amazon.com/Constructing-Quantum-Mechanics-Scaffold-1900-1923/dp/0198845472/?tag=pfamazon01-20 https://www.amazon.com/Constructing-Quantum-Mechanics-Arch-1923-1927/dp/0198883900/?tag=pfamazon01-20

https://www.quantamagazine.org/never-repeating-tiles-can-safeguard-quantum-information-20240223/

The Wikipedia article on Quantum Gravity reads: "The observation that all fundamental forces except gravity have one or more known messenger particles leads researchers to believe that at least one must exist for gravity. This hypothetical particle is known as the graviton" To which... yikes...

Using the time derivative of an operator, and expanding out, I got to this: $$\frac{d}{dt}\langle\hat{x}\hat{p}\rangle=\frac{i}{\hbar}\left\langle\left[\hat{H},\hat{x}\hat{p}\right]\right\rangle+\left\langle\frac{\partial}{\partial t}\left(\hat{x}\hat{p}\right)\right\rangle$$ Expanding using...

a and b were fairly easy to solve; but the c part which actually demands the probability! How are we suppose to fetch the value if the function can't even be normalized; I tried to make some assumptions like making the system bounded; but I don't think that it's the right way to do so... What...