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 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Although not unanimously, many agree that the concept of "wave-particle duality" is outdated.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})$$
I have some doubts about...
Consider the state ##\ket{\Psi} = \sum_{1 \leq n_{1} \leq n_{2} \leq N} a(n_{1},n_{2})\ket{n_{1},n_{2}}## and suppose $$|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...
By the results of the photoelectric effect experiment, the photoelectric effect does not occur at all if the frequency of the light source is below a certain value.
We have the Work Function for a metal. Why when the energy of the photons of the light source is W/2, we don't have the...
Hey, I was just contemplating career opportunities after my Undergrad. I am slightly interested in theoretical physics but I can't imagine doing it the rest of my life. My main interests are nano-photonics and quantum technologies and I am planning to do research in these fields. I am not...
Hi, I am new here. I expect that most people will find my approach to science interesting because I do not do standard physics. I do SUSY inversion and the He-BEC DE DM model corresponding to a revision of quark charge calculations giving rise to Baryonic symmetry.
I'd like to hear your professional opinion on and experience with using Quantum Field Theory for the Gifted Amateur by Tom Lancaster and Stephen J. Blundell as a self-study textbook. Thank you.
I'm reading the article on the Many Worlds Interpretation in the Stanford Encyclopedia of Philosophy. I'm keeping up well, but this excerpt uses things I'm very unfamiliar with:
I guess some characters weren't recognized. It's Section 3.6 here. I'm somewhat familiar with Wigner's Friend, but...
Between the walls of a finite well, the solution to the time independent Schrodinger equation is a combination of sines and cosines. Outside the walls where E - Uo is positive, the solutions are exponential functions. Why?
This is the given circuit:
I think to add another Cnot on the right with a1 as control and a0 as target, to set initial states of a0 an a1 both |0⟩, and to measure the a0. If a0=|0⟩ then b0=b1, and vice versa.
Is it correct?
Hi, my name is Kennard Callender. I am an independent scientist from Panama working on the foundations of quantum mechanics and relativity. I look forward to meeting people who desire to understand nature at its most fundamental level and who can help me polish my work.
Hi guys I have a question for you. Virtual particles can appear anywhere and when they have enough energy they turn into real. And if it happens long enough in a vacuum, will it remain a vacuum? If not, then is matter infinite?
The title is from a great book by Eric Kraft, who plays around with one's physical-being in elemental terms in an excellent novel. He is very funny.
To get down to my question: Do electrons or photons on anything move faster than the speed of light?
I just learned about the Stern-Gerlach experiment and have some questions:
1: clearly there's no objective "up" or "down"--the directions are measured relative to the magnetic field, correct? And well always find just 2 spots of equal and opposite distance on the detector, implying the magnetic...
How can we link the band gap to lattice spacing?
For (a), if we purely do dimension analysis, then I would guess $$a=\frac{\hbar c}{E_g}$$. But what's the reason behind this answer, and will the true lattice spacing be larger or smaller?
For (b), I guess $$\lambda=\frac{\hbar c}{E_g}$$ due to...
If I have a brittle piece of rock and hit it with a hammer, can a round ball split of in some universe, verses in our universe a piece with rugged ends always form? If so, why do we always, in our universe seem to get "expected" results? Why dont strange things happen here sometimes? Why is our...
Let's assume that there is a closed box, with mass M. There are some random quantum processes inside it, say radioactive decay. Let's assume that we can manipulate the decay from the outside somehow, thus 'putting information' into the box. Can that affect its mass?
Can you swap out the RNG that is the wave function collapse with a suitable deterministic chaotic process that matches the wave function (squared)?
I can picture a multi leg pendulum swinging around drawing out the wave function. The point where you measure is the point the pendulum was at.
Is...
Hello Dear Physicists,
I know this question probably discussed many times before. But I need a clear answer about this setup in case there is no beam splitter.
What is gonna happen in this situation? My classical intuitions say I will see a correlated interference pattern on both screens(or...
ATTEMPT AT SOLUTION: I understand if looking for positive this will be +hwo/2 (hbar) for Sz so must find |a|^2. and if looking for negative this will be -hwo/2 (hbar) so must find |b|^2. If asked to find say Sx and original question in Sz, we must find new eigenstates associated with this state...