Quantum mechanics Definition and 994 Threads

I came across this article at physicsworld.com which has the headline "Quantum mechanics defies causal order, experiment confirms". https://physicsworld.com/a/quantum-mechanics-defies-causal-order-experiment-confirms/ The actual experiment is described here: https://arxiv.org/abs/1803.04302 I...

I have started going through the Quantum Mechanics 8.04x and 8.05x from MIT in edx by prof. Barton Zwiebach. I am enjoying them. 8.04x 1. https://courses.edx.org/courses/course-v1:MITx+8.04.1x+3T2017/course/ 2. https://courses.edx.org/courses/course-v1:MITx+8.04.2x+3T2017/course/ 3...

(a) and (b) are fairly traditional, but I have trouble understanding the phrasing of (c). What makes the infinite dimensionality in (c) different from (a) and (b)?

Homework Statement [/B] A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x) = (1/2) kx2 . If the spring constant of the oscillator is suddenly doubled, then the probability of finding the particle in ground state of new potential will be? (A)...

I have found this one that looks perfect: https://www.amazon.com/dp/331999929X/?tag=pfamazon01-20 THe problem is that it has not been published yet :( , but I can't believe there is no other book on the subject. What I want is to solve numerically the Schrodinger equation with no special...

Homework Statement I wish to solve this integral $$b_{lm}(k) = \frac{1}{2(\hbar)^{9/4}(2\pi)^{5/2}\sqrt{\sigma_{px} \sigma_{py} \sigma_{pz}}} \int_{\theta_k = 0}^{\pi}\int_{\varphi_k = 0}^{2\pi} i^l \text{exp}\left[ - \frac{1}{(2\hbar)^2}\left(\frac{(k_z - k_{z0})^2}{\sigma_{pz}^2} + \frac{(k_y...

Hi. I want to learn - amateurishly - Quantum Mechanics, and General Relativity, but my experience with Physics is very small. I want to ask, what should I learn - what books should I read - before I start to learn those theories? Sorry for my english.

Homework Statement Sakurai, problem 1.11 A two-state system is characterized by the Hamiltonian $$ H = H_{11} | 1 \rangle \langle 1| + H_{22} | 2 \rangle \langle 2| + H_{12} \left[ | 1 \rangle \langle 2| + | 2 \rangle \langle 1| \right] $$ where ##H_{11}##, ##H_{22}##, and ##H_{12}## are real...

I liked his Group Theory book. Now he wrote a QM book. No-Nonsense Quantum Mechanics: The Ultimate No Holds Barred Guide To The Quantum World

Homework Statement For massless particles, we can take as reference the vector ##p^{\mu}_R=(1,0,0,1)## and note that any vector ##p## can be written as ##p^{\mu}=L(p)^{\mu}_{\nu}p^{\nu}_R##, where ##L(p)## is the Lorentz transform of the form $$L(p)=exp(i\phi J^{(21)})exp(i\theta...

Homework Statement The SO(3) representation can be represented as ##3\times 3## matrices with the following form: $$J_1=\frac{1}{\sqrt{2}}\left(\matrix{0&1&0\\1&0&1\\ 0&1&0}\right) \ \ ; \ \ J_2=\frac{1}{\sqrt{2}}\left(\matrix{0&-i&0\\i&0&-i\\ 0&i&0}\right) \ \ ; \ \...

Homework Statement What will momentum measurement of a particle whose wave - function is given by ## \psi = e^{i3x} + 2e^{ix} ## yield? Sketch the probability distribution of finding the particle between x = 0 to x = 2π. Homework Equations The Attempt at a Solution The eigenfunctions of...

Hello! I got a bit confused about the fact that the whole the description of spin (and angular momentum) is done in the z direction. So, if we are told that a system of 2 particles is in a singlet state i.e. $$\frac{\uparrow \downarrow -\downarrow \uparrow }{2}$$ does this mean that measuring...

Homework Statement We are investigating hydrogen in a plasma with the temperature 4500 ºC. Calculate the probability per atom and second for stimulated emission from 2p to 1s if the lifetime of 2p is 1.6 ns Homework Equations Planks radiation law: ##\rho (f) = \frac{8* \pi...

How electron revolves around orbitals? Is the velocity uniform or accelerated?

Hello. I've been struggling for a day with the following problem on Quantum coherent states, so I was wondering if you could tell me if I'm going in the right direction (I've read the books of Sakurai and Weinberg but can't seem to find an answer) 1. Homework Statement *Suppose a Schrödinger...

I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...

I think this could be an interesting discussion (unless I'm just totally off base): I don’t think were looking at things right in the atomic world. We represent everything as this wave particle duality which is not incorrect but is a great way to visualize particles and forces and their...

Homework Statement Consider two pairs of operators Xα, Pα, with α=1,2, that satisfy the commutation relationships [Xα,Pβ]=ihδαβ,[Xα,Xβ]=0,[Pα,Pβ]=0. These are two copies of the canonical algebra of the phase space. a) Define the operators $$a_\alpha =...

Hi. I just received a copy of Ballentine's "Quantum Mechanics: A Modern Development" ordered from Amazon, after I heard well of it in this site. I'm wondering what edition I've bought: the one I've got has a white hardcover, and its ISBN is 9789810227074. Does someone ever used this edition? Why...

I recently watched a video where Sean Carroll talked about QM and multiverses 1/ Could you please explain: Where does all the energy come from to drive all these universes. Surely this must take an enormous amount of energy to drive a multiverse system (infinite). Does each universe...

Greg Bernhardt submitted a new PF Insights post Why the Quantum | A Response to Wheeler's 1986 Paper Continue reading the Original PF Insights Post.

I have been taking many online courses. In the prerequisites for many courses, it has been mentioned, "basic" quantum mechanics. It has become important to define where the boundary of basic ends and the advanced level starts, though I believe that is not well defined. I have been studying QM...

Supposing the Many Worlds interpretation of QM is true... If a branching occurs during what we perceive is a wave function collapse, why would this be perceptible to us as probabilties? Wouldn't we just branch, leaving it just as imperceviable as the passage of time? That is, it just happens...

Are there any projects I can build? What are the applications of QM in electrical engineering?

Hi all, I've always regarded the coupling Hamiltonian for a bosonic cavity mode coupled to a two-level fermionic gain medium chromophore to be of the form, $$H_{coupling}=\hbar g(\sigma_{10}+\sigma_{01})(b+b^{\dagger})$$, where ##b## and ##b^{\dagger}## and annihilation and creation operators...

I lost my book on Quantum mechanics! It was published in the late 80s or early 90s in England. Title: Quantum Mechanics. The book used algebra with more advanced math in the appendices. If you know the author , please reply. Thanks!

ER=EPR, black hole complementary, firewalls, vacuum entanglement etc.. Where do I begin studying these new ideas? I have a solid understanding about Quantum Field Theory and the classical theory of gravity, but no knowledge of string theory. Are there some advice or book recommendations anyone...

I’m having a hard time, as I begin learning QM, knowing what it applies to, if I can put it that way. Is QM the rules that describe how the particles of the Standard Model interact with each other? Or what is the best way to understand the relationship between what one studies when one studies...

Can quantum cellular automata/quantum game of life simulate quantum continuous processes in the continuous limit? At the end of this article: https://hal.archives-ouvertes.fr/hal-00542373/document it is said that: "For example, several works simulate quantum field theoretical equations in the...

:rolleyes: I would like to find a free online course, not too hard. I have minors in math and physics, but have been away for awhile. Maybe something on youtube. If someone knows of a decent course that I could educate myself with I would appreciate any info on it. Thanks in advance...

In Special/General Relativity invariance of a space-time interval is just so important. But in Quantum Mechanics, be it non-relativistic or QFT, there seems to be no such parallel. I have always noticed this. I have some ideas about the reason: 1 - it's not part of the theory to have a...

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Homework Statement Real atomic nuclei are not point charges, but can be approximated as a spherical distribution with radius ##R##, giving the potential $$ \phi(r) = \begin{cases} \frac{Ze}{R}(\frac{3}{2}-\frac{1}{2}\frac{r^2}{R^2}) &\quad r<R\\ \frac{Ze}{r} &\quad r>R \\...

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.