In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.
For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.
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...
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...
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??
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...
Ask any informed man on the street for the quantum mechanics explanation of light and his answer would probably be something like this:
“Light as it travels from point A to point B is not something real, it exists as an abstract mathematical wave function that exists everywhere and nowhere...
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...
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
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$$
Expanding using...
a and b were fairly easy to solve; but the c part which actually demands the probability! How are we suppose to fetch the value if the function can't even be normalized; I tried to make some assumptions like making the system bounded; but I don't think that it's the right way to do so... What...
I was / am trying to derive the energy shift resulting from the normal Zeeman-Effect by coupling the Hamiltonian to the external field ##\vec{A}##, that carries the information about the field ##\vec{B}## via ##\vec{B} = \nabla \times \vec{A}##. Let ##q = -e## be the charge of the electron and...
It is cited here, and here like so:
And here
[edit] - and here
The full quote from the paper I cited:
I don't see how this paper is not a paper about the no boundary proposal.
and how is it known that the two photons are entangled in the first place? I mean before measuring how do you know that you have the correct two photons?
I have this following Gaussian wavefunction.
I found the constant C to be $$\sqrt{\sqrt{\frac{2 \alpha}{\pi}}}$$.
Now they're asking me to find the normalized impuls wavefunction $$\phi(p)$$. I tried to use the fourier transform relation
$$\phi (p) = \int e^{-\frac{i ( p x)}{\hbar}} \Psi...
I cannot find a clear answer on the following beginner’s question on some QM fundamentals:
Suppose we have two particles, A and B. Let’s say we generated these as (or otherwise entangled them as) an entangled pair with opposite/orthogonal states. Perhaps horizontally and vertically polarized...
Starting from this link my understanding of Bell inequality proof goes as follows:
Suppose we have a model of local pre-determinate hidden variables for QM. This amounts to say QM objects are in pre-determinate given states even if we do not measure it. Locality just means that spacelike...
Just a guy with huge Curiosity Quotient, in subjects ranging from Astronomy to Quantum Physics, to Geology and Ancient Mythology, Chemistry to Science Fiction & Fantasy, and finally Science in General.
Hi all,
I was wondering if there was a reference/textbook where the degenerate perturbation calculation for the Transverse Ising model was treated fully. I want to better understand how in the weak magnetic field limit, the ground state degeneracy only lifts at N'th order in perturbation theory...
Neil deGrasse Tyson has been a great "goto" and respected physicist for me to follow online. I've read Einstein's biography and have been fascinated with the world as theorized by some of the greatest minds and proofs.
Recently, I've come across a name I've never known. Admittedly, this is a...
An electron requires an "exact" wavelength photon to transition from one level of an atom to another. Yet the wavelength of a photon has a a continuous probability distribution, implying that the point probability of achieving an exact wavelength is zero. One can only talk meaningfully about...
Hello,
I understand the photoelectric effect, its importance, and the basic theory. But I have a few questions:
1) One photon "can" free only a single electron, correct? However, it is not certain that if we shine exactly 10 photons (frequency? ##f_0##), that 10 photoelectrons will be free...