So, in a rare instance I actually read APS News, I came across “New Experiment Suggests Imaginary Numbers Must be Part of Real Quantum Physics.” In November 2022, Volume 31, Number 10.
Since complex numbers are isomorphic to a real 2x2 matrix algebra, I was confused how such a claim can be...
Hi,
I'm working on a problem where I need to find the different energies allowed for a potential, and I found this link https://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html,
which is similar of what I'm doing. I'm using mathematica to find the values of E.
However, I'm not sure how...
I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.
Alain Aspect, John Clauser & Anton Zeilinger have rightfully received the Nobel prize for their contributions to quantum information, as they were three of the main pioneers of quantum information.
However, is it now impossible or very unlikely that other physicists working on this field (e.g...
The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem:
1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...
Hi,
I have hard time to really understand what's a stationary state for a wave function.
I know in a stationary state all observables are independent of time, but is the energy fix?
Is the particle has some momentum?
If a wave function oscillates between multiple energies does it means that the...
I found a paper (https://arxiv.org/pdf/astro-ph/0411299.pdf) which talks about quantum systems emitting energy due to spacetime expansion. Is this true or only a hypothesis?
I read in the following book A history of the sciences by Stephen F. Mason. About the discovery of the electron the write what I attached in the picture.
I wonder what do these positive rays traveling in the opposite direction they talk about consist of? Some ions or what? I understand that the...
Hello guys, I don't know if this is the right place to ask, so please be kind :/
I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%.
When I asked about the remaining...
In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is...
What is it of the photon that gets polarized from a quantum mechanical perspective? In the classical perspective it is often thought that it is the oscillating electric field that gets polarized. But in the quantum case: Is it the de Broglie wave function? Or is it the spin and in case it is the...
I am reading this chapter 3 from the book called The Quantum Vacuum by P.Milonni.(Attached in the pdf, look at chapter 3.2 Spontaneous emission)There they say that spontaneous emission is due to both quantum fluctuations and radiation reaction. They say the transitions induced by the quantum...
Hello, I'm hoping someone can help me understand a statement in Sakurai Modern Quantum Mechanics (3rd edition).
In particular, in the section that describes free particle in infinite spherical well (page 198, section 3.7.2), after the text has shown that for a given ##l## value, the energy...
[Mentor Note -- thread moved from the schoolwork forums to the technical forums]
Homework Statement:: Tentative Note and summary on the origin and the evolution of information in the universe.
Relevant Equations:: none
As a teacher of physics I got many questions asked by my students when...
So this expression is apparently in Sz basis? How can you see that?
How would it look in Sy basis for example?
The solution is following. They are putting Sz as a basis, bur how do you know that Sz is the basis here?
Thanks
I can't figure out how they get i/sqrt(2) for normalisation of c1. Why is it a complex number? If I normalise c1 I just get 1/sqrt(2) because i disappears in the absolute value squared.
Thanks
I was reading this paper from George Smoot (https://arxiv.org/abs/1003.5952) where he assumes the holographic principle as true and conjectures that our universe would be encoded on the "surface" of an apparent horizon as the weighted average of all possible histories. In that way, there would...
I'd like to understand how gravity does not combine with quantum mechanics. At least there is no accepted theory of quantum gravity, so I assume it is not solved? I'm only starting to learn QFT and eventually GR. Maybe, someone can already outline where those theories fail to combine and comment...
I am learning Dirac notations in intro to quantum mechanics. I don’t understand why the up arrow changes to down arrow inside the equation in c).
My own calculation looks like this:
I have a lecture slide that shows how to find S_x and S_y. I get all the steps except the last row.
Where did 1/2 come from? I think my linear algebra needs polishing.
Thanks!
I'm wondering about some aspects about black holes (BH) and singularities, but since all my questions have to do mostly with quantum mechanics, I placed this thread in here.
OK, let's assume there IS a singularity in the middle of a BH.
A) Pauli exclusion principle (PEP) says no two fermions...
As per title and the TL;DR, I'm curious if there could be some truth in these statements of the headlines I had read recently or are they just sensationalist fluff.
Personally, I find these statements very hard to believe. In fact, impossible to believe. But I'm not a QM expert, not even an...
Listen to the following arguments:
Earth's orbit isn't perfect ellipse because classically there is the gravitational field of moon and possibly of Mars and Venus which affect it
According to general relativity isn't perfect ellipse because there is the curvature of space time which doesn't...
In the paper
C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573
about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...
David Wallace, The sky is blue, and other reasons quantum mechanics is not underdetermined by evidence, Manuscript (2022). arXiv:2205.00568.
From the Abstract:
''I argue that there as yet no empirically successful generalization of''
[Bohmian Mechanics and dynamical-collapse theories like the...
In a) I get that T should be largest where V_0 is least wide, because when V_0 is infinitely wide the particle would be fully reflected.
But I don't get how height in b) and energy levels height in c) correlates to T and R.
Is it because of their k? I get the opposite answer from the correct...
I have solved c), but don’t know how to solve the integral in d.
It looks like an integral to get c_n (photo below), but I still can’t figure out what to make of c) in the integral of d).
I also thought maybe you can rewrite c) into an initial wave function (photo below) with A,x,a but don’t...
I have a problem with this Hamiltonian: two identical particles of mass ##m## and spin half are constrained to move on the surface of a sphere of radius ##R##. Their Hamiltonian is ##H=\frac{1}{2}mR^2(L_1^2+L_2^2+\frac{1}{2}L_1L_2+\frac{1}{2}S_1S_2)##. By introducing the two operators...
I have approached this question step by step as shown in the image attached.
I request someone to please guide if I have approached the (incomplete) solution correctly and also guide towards the complete solution, by helping me to rectify any mistakes I may have made.
I'm still unsure how to...
I am considering tunnel effect with a potential barrier of a certain height that is ##\neq 0## only for ##0 \le x \le a## . I write the Hamiltonian eigenfunctions outside the barrier as:## \psi_E(x)=\begin{cases}
e^{ikx}+Ae^{-ikx} \quad \quad x \le0 \\
Ce^{ikx} \quad \quad x\ge a \\...
If I have two identical particles of ##1/2## spin, for Pauli's exclusion principle all physical states must be antysimmetrical under the exchange of the two particles, so ##\hat{\Pi}|\alpha\rangle=-|\alpha\rangle##. Now, let's say for example this state ##\alpha## is an Hamiltonian eigenfunction...
In a central potential problem we have for the Hamiltonian the expression: ##H=\frac{p^2}{2m}+V(r)## and we use to solve problems like this noting that the Hamiltonian is separable, by separable I mean that we can express the Hamiltonian as the sum of multiple parts each one commuting with the...
Just earlier today i was practicing solving some ODEs with the power series method and when i did it to the infinite square well i noticed that my final answer for ##\psi(x)## wouldn't give me the quantised energies. My solution was
$$\psi(x) = \sum^{\infty}_{n=0} k^{2n}(\cos(x) + \sin(x))$$...
Very basic question here, about statistical independence in quantum mechanical experiments. The quote from PD below is what prompted the question.
When we talk about "some kind of pre-existing correlation" are talking about a simple correlation in the sense of the correlation of sunglasses and...
Summary:: I understand the consensus on PF about studying for knowledge and not merely for "cracking Semester Exams" but I urge you all to go through below thread before attaching to that feeling in my case.
Hi.
So I have my Exams on Intro QM approaching very soon, which will be a combination...
Below I have attached an image of my possible solution. I have replaced all the relevant limits. For some reason, I am getting the final value for (i) part as ψ(x)= with an additional √2pi in the denominator. Have I made any errors or is it fine if I take it within the constant A..
In...
I need to know if I have solved the following problem well:
A spin-less particle of mass m is confined to move on the surface of a cylinder of infinite height with a harmonic potential on the z-axis and Hamiltonian ##H=\frac{p_z^2}{2m}+\frac{L_z^2}{2mR^2}+\frac{1}{2}m\omega^2z^2## and I need to...
I have read about several approcahes to bypass some classical restrictions to quantum facts such as the electron being in a torus-like shape to avoid ,the greater than speed of light, rotation paradox . Could you recommend websites , sources or books that give good classical analogy to quantum...
To solve a particle on a sphere problem in quantum mechanics we get the below equation :##\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2} \theta}\right] \Theta(\theta)=-A \Theta(\theta) ##
To solve this differential equation, we...
Hello there, for the above problem the wavefunctions can be shown to be:
$$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$
Here ##b = \sqrt{1 +...
I've tried figuring out commutation relations between ##L_+## and various other operators and ##L^2## could've been A, but ##L_z, L^2## commute. Can someone help me out in figuring how to actually proceed from here?
Let ##|l,m\rangle## be a simultaneous eigenstate of operators ##L^2## and ##L_z## and we want to calculate ##\langle l,m|cos(\theta)|l,m'\rangle## where ##\theta## is the angle ##[0,\pi]##. It is true that in general ##\langle l,m|cos(\theta)|l,m'\rangle=0## ##(1)## for the same ##l## even if...
I am very interested in quantum mechanics/physics and i keep seeing the Heisenberg uncertainty principle and its making me think about other forms of viewing particles.
We traditionally use Photons to view something (our eyes), or other forms of radiation/particles, but i know that merely...