Quantum mechanics Definition and 994 Threads

Greg Bernhardt submitted a new PF Insights post How to Better Define Information in Physics Continue reading the Original PF Insights Post.

Hi all, I'm trying to find a mathematical way of showing that given a complete set $$\left |a_i\right \rangle_{i=1}^{i=dim(H)}∈H$$ together with the usual property of $$\left |\psi\right \rangle = ∑_i \left \langle a_i\right|\left |\psi\right \rangle\left |a_i\right \rangle ∀ \left...

Hi. I bought Messiah's "Quantum Mechanics" because it was at an excelent price from Dover. But, even though it was considered a Bible of quantum mechanics until recently, people consider it outdated now. Is it no longer comprehensive? I intend to read on relativistic quantum mechanics and...

Homework Statement Find the wave packet Ψ(x, t) if φ(k) = A for k0 − ∆k ≤ k ≤ k0 + ∆k and φ(k) = 0 for all other k. The system’s dispersion relation is ω = vk, where v is a constant. What is the wave packet’s width? Homework Equations [/B] I solved for Ψ(x, t): $$\Psi(x,t) =...

What is exactly Weizsäcker's ur-alternatives theory? How is it related to digital physics theories? Is it related to pancomputationalism? Does it defend that a universe can be described as being fundamentally made of qubits? Would this mean that that universe would be fundamentally made by...

Homework Statement Does the n = 2 state of a quantum harmonic oscillator violate the Heisenberg Uncertainty Principle? Homework Equations $$\sigma_x\sigma_p = \frac{\hbar}{2}$$ The Attempt at a Solution [/B] I worked out the solution for the second state of the harmonic oscillator...

I find the de Broglie-Bohm pilot wave theory interesting but what I still feel missing in the descriptions I could find so far is that it reformulates what we already know but nobody speaks of new testable predictions that could eventually distinguish it from other interpretations (such as a new...

These are from Griffith's: My lecture note says that I am having quite a confusion over here...Does the ##\Psi## in the expression ##\langle f_p|\Psi \rangle## equals to ##\Psi(x,t)##? I understand it as ##\Psi(x,t)## being the component of the position basis to form ##\Psi##, so...

I was wondering how the rules work for observation in a quantum system. Particularly, about what happens if two separate entities try measuring at the same time. And also, what kinds of interactions are happening all the time that are considered measurements, for example in quantum...

Homework Statement Consider scattering of a particle of mass ##m## on the potential $$U(r) = \begin{cases} 0, & r \geq b\\ W, & r < b \\ \end{cases}$$ Where ##W## is some arbitrary chosen constant, and the radius ##b## is considered a small parameter. Find the cross section ##\sigma## in the...

I was solving an exercise from Cohen's textbook, but then I got stuck in this question. "Let ψ(x,y,z) = ψ(r) the normalized wave function of a particle. Express in terms of ψ(r) the probability for: b) a measurement of the component Px of the momentum, to yield a result included between p1...

Homework Statement The Attempt at a Solution [/B] Hi All, I'm having trouble answering part (f) of the above question. I have managed parts (d) and (e) fine but am not sure how to proceed with part (f). I am pretty sure that the amplitude of the reflected wave in region 1 will be zero...

Homework Statement Have to read a paper and somewhere along the line it claims that for any distinct ## \ket{\phi_{0}}## and ##\ket{\phi_{1}}## we can choose a basis s.t. ## \ket{\phi_{0}}= \cos\frac{\theta}{2}\ket{0} + \sin\frac{\theta}{2}\ket{1}, \hspace{0.5cm} \ket{\phi_{1}}=...

Hello all, I have only seen this paper brought up here once before based on the search function 2 years ago, and the thread devolved into something off topic within the first page. I am asking in reference to this paper: https://arxiv.org/pdf/1604.07422.pdf Which claims to show that single...

It's rare to encounter concrete, numerical examples of what is being taught about Relativity, Quantum Mechanics.. On the other hand there's plenty of numerical examples in the undergraduate general physics textbooks, for instance problems of mechanics. As for General Relativity I did find only...

What is the nonperturbative approach to quantum mechanics as opposed to perturbative one? When does the latter method fail and one has to apply nonperturbative approach? Please keep your discussion confined within non-relativistic quantum mechanics.

I just came across the following paper: Gisin, N. (2011). Impossibility of covariant deterministic nonlocal hidden-variable extensions of quantum theory. Physical Review A, 83(2), 020102. proving that, under sensible hypotheses, nonlocal hidden variable theories for relativistic quantum...

If atom are invisible then how can one say that atoms are made up of electrons nucleus and quasi particles.

In Zettili's Quantum Mechanics, page 477, he wants to determine the energy and wave function of the ground state of three non-interacting identical spin 1/2 particles confined in a one-dimensional infinite potential well of length a. He states that one possible configuration of the ground state...

Imagine a system of 1 particle in a superposition of eigenstates of some operator(s). If one were to make a measurement of a property of that particle, how is the operator (or observable) "picked" so that the wavefunction collapses into an eigenstate of said operator? In other words, how do one...

Suppose we have a quantum system ##Q## with an initial state ##\rho^{(Q)}##. The measurement process will involve two additional quantum systems: an apparatus system ##A## and an environment system ##E##, hence giving the initial state of the system ##\rho^{(AEQ)} = \rho_{0}^{(AE)}\otimes...

I was reading an article about holographic principle and M-cosmology and how could they be used to interpret QM mechanics. But there's a part where it talks about holographic principle in a strange way to me. What does this article mean with this?: "Since for the participant observer the...

Yesterday, I was solving an exercise from Cohen-Tannoudji's book - Quantum Mechanics -, but then I got stuck on the second question that the exercise brings. I wonder if you guys could help me, and here is the exercise: "Using the relation <x|p> = (2πħ)-½ eipx/ħ, find the expressions <x|XP|ψ>...

Just for a bit of fun, which theory , relativity or quantum mechanics has the most accurate ( i.e to how many decimal places confirmation between theory and experiment) measurement ever made?

Just a thought I had one day, but the general idea I've heard is that quantum mechanics has a random property to it. The number Pi is apparently a number without any sort of apparent pattern to it either, seemingly random? Could these two things somehow be related? For example somehow...

I've been reading about self teaching physics (mainly because the college curriculum is too slow to get me to any meaningful level of understanding at the end of four years), and an issue was brought up about lack of intuition in quantum mechanics/GR, and depending too much on the math. I was...

When we look at the cars on the road, it appears like where they are driving is random, their directions appear as random. But the drivers don't drive into random directions. It appears random to us because we don't know the thoughts and intentions of the drivers. If we knew almost everything...

Hello everyone! I am working on a quantum mechanics research paper and I need to interview one person. It can be electronically or even in a place like this. I just need one person to answer a few simple questions and to describe their qualifications that prove they are a reliable source for...

Homework Statement The photon is normally assumed to have zero rest mass. If the photon did have a tiny mass, this would alter the potential energy the electron feels in the hydrogen atom (due to the Coulomb interaction with the proton). The potential then becomes yukawa potential...

The field of quantum mechanics was launched with scientists struggling to understand blackbody radiation. My question is: what is the source of this observed radiation? Is it the nuclei in the matrix of the metal jiggling around ever more energetically as you heat up the metal? Or is it the...

The question is prompted by a claim raised in another thread that "There is good reason (theoretically) to believe that linearity fails at high enough energies." I've put this with an A prefix because it is going to be about some damned difficult maths, I know. But please try to avoid the...

Greg Bernhardt submitted a new PF Insights post "Classical Physics Is Wrong" Fallacy Continue reading the Original PF Insights Post.

In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##. Given the state ##\omega## we can consider the GNS construction...

I am not able to understand why compounds have colour. I have read that it is due to excitation of electrons from one atomic/Molecular orbital to another because of which certain wavelengths are absorbed, And we can see the "complementary colour" of those wavelengths. What I don't understand is...

Hello PF, I am currently taking a course on quantum mechanics that is following Griffiths' textbook (page by page). The first exam in the course coincided with two other courses (analysis and probability theory) and so I did lack a bit of training while doing it (the required material was from...

I know little about QED, QCD, and whatever the corresponding theory for the weak force is, and of course virtually nothing about the quantized theory of the gravitational force, which mostly doesn’t exist, so the following arguments and questions may be somewhat wrongly based where they refer...

I'm relatively new to Quantum Mechanics (QM), so please correct me if I'm wrong at any point. As I currently understand QM, everything exists as a non-tangible wave consisting of all possible outcomes until observation forces that wave to collapse into a single outcome, which becomes real. Is...

Consider the following examples: 1) combine a spin 1/2 state (with 2D Hilbert space and three spin 0 states (each with 1D Hilbert space). The resultant state is in 3D Hilbert space. 2) combine the same spin 1/2 state (with 2D Hilbert space and one spin 0 state. The states in (1) and (2)...

The term "state" in quantum mechanics is not generally agreed across the physics community. Some physicists consider it to be synonymous with "state preparation procedure". Others find this too restrictive, as it would exclude states not prepared in a laboratory. For example my nose is not...

Is it possible for me to do cosmology and quantum mechanics as a joint degree at uni? If so where and does it cost extra? I’ve been wondering for a whole and I’m not sure where to look.

I am going to be doing a high school senior research project on how Quantum Physics will change the world in the future. Basically my current idea is to describe what quantum mechanics is, and then give examples that I explain and I state how they will change the world and the estimated time...

Studying QFT on curved spacetimes I've found the algebraic approach, based on ##\ast##-algebras. In that setting, a quantum system has one associated ##\ast##-algebra ##\mathscr{A}## generated by its observables. Here we have the algebraic states. These are defined as linear functionals...

This ties into this thread https://www.physicsforums.com/threads/i-want-to-know-the-exact-problems-of-merging-gr-and-qm.939509/ , I would like to know SR/GR's opinion of QM/QFT. I need both sides of the story.

This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...

Hi all, so I'm not sure if what I'm asking is trivial or interesting, but is there any general or canonical way to interpret say, The follwing operator? (Specifically in the study of quantum mechanics): A = 1/(d/dx) (I do not mean d-1/dx-1, which is the antiderivative operator ) How would...

Hi all, There is this question; Firstly, I am new to quantum mechanics and there are a lot of terms I am unfamiliar with. So there is this question that asks me to develop a method to reconstruct state and I have no clue how I should start with. Any help or steps to solve this type of...

[Mentors' note: one short paragraph of speculation in violation of the Physics Forums rules has been removed from this post] Follow the link below to play with my experimental sandbox. The rest of this post includes some instructions for use and then observations and a little bit of theory...

hi, do the translation operator commute with parity operator?

It is the resolution given by my thermal interpretation, and this resolution is valid (independent of the thermal interpretation) even without being accepted. Bell assumes that measurement outcomes follow strictly and with infinite precision Born's rule for a von Neumann measurement. But the...

I am not sure whether this is posted before but it looks really good to me. http://www.tcm.phy.cam.ac.uk/~bds10/aqp.html