Quantum mechanics Definition and 994 Threads

Hi, I'm an undergrad, following my very first serious course in QM. We're following Griffith's book, and so far we're staying close to the text in terms of course structure. Griffiths starts out his book by postulating that each and every state for any system \Psi must be a solution to the...

Greg Bernhardt submitted a new blog post Wigner's Friend Continue reading the Original Blog Post.

Hi, I'm sorry if this question has already been answered somewhere and I'm just too incompetent to find it, buuut: As the title already says, I really do not get that part of quantum physics (if you can even say I'm getting ANY part at all...). As I searched all Google for an answer I just...

I study on quantum mechanics and I have question about operator. In one dimension. How do we know ## \hat{x} = x## and ## \hat{p}_{x} = -i \bar{h} \frac{d}{dx} ## When schrodinger was creating an equation, which later called "the schrodinger equation". How does he know momentum operator equal...

Does Hardy's paradox show that all realist interpretations cannot be made lorentz invariant? Or is it just realist hidden variable theories?

Homework Statement For the canonically quantized operators, what are the step in between? how do you get the answer iħ? [q^,p^]=iħ q^ is the coordinate and p^ is the momentum.

Greg Bernhardt submitted a new blog post The Unreasonable Effectiveness of the Popescu-Rohrlich Correlations Continue reading the Original Blog Post.

In this video, at around 37:10 he is explaining the orthogonality of spherical harmonics. I don't understand his explanation of the \sin \theta in the integrand when taking the inner product. As I interpret this integral, we are integrating these two spherical harmonics over the surface of a...

hi, I’ve been walking through posts on this forum, and found plenty of book recommendations for QM. My problem is, I haven’t had enough practice in a long while. I could go over Solved Problems in e.g. Galitsky, or Gasiorowitz, but they seem to be a little far from what I want to test...

Let me present what I think is the understanding of a particular situation in quantum mechanics, and ask people to tell me whether I am right or wrong. To say that everything happens randomly in QM would be misleading at best. We get at least statistical prediction. But discussions such as the...

We are all familiar with Heisenbergs uncertainty principle. When we determine the position of a particle or wave, the uncertainty of momentum reach infinity. So let's say I have a machine that measures the position very very precisely. Then the uncertainty of this non-moving particles momentum...

1. The problem statement I want to write the angular momentum operator ##L## for a 2-dimensional harmonic oscillator, in terms of its ladder operators, ##a_x##, ##a_y##, ##a_x^\dagger## & ##a_y^\dagger##, and then prove that this commutes with its Hamiltonian. The Attempt at a Solution I get...

Hi! I want to know under what conditions the operator expectation values of a product of operators can be expressed as a product of their individual expectation values. Specifically, under what conditions does the following relation hold for quantum operators (For my specific purpose, these are...

Homework Statement Okay, so the question I'm trying to solve is to find the quantized energies for a particle in the potential: $$V(x)=V_0 \left ( \frac{b}{x}-\frac{x}{b} \right )^2$$ for some constant b. The Attempt at a Solution I am following along with the derivation of the quantized...

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?

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...

: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) =...