Qm Definition and 1000 Threads

I'm starting this thread because @PeterDonis suggested in the other thread that time is treated diferently in quantum field theory and relativistic quantum mechanics/ ordinary quantum mechanics. I'd like to know specifically how is it treated in QFT and in relativistic Quantum Mechanics. Of...

I realize this type of question has been asked elsewhere on competitor websites but I want to make it more precise. Usually, the person asks if anything in QM is possible to which the answer is no, for example, a photon cannot have spin 0, hence some things in QM are impossible. But what about...

1. Problem Recall that we defined linear equations as those whose solutions can be superposed to find more solutions. Which of the following differential/integral equations are linear equations for the function u(x,t)? Below, a and b are constants, c is the speed of light, and f(x,t) is an...

Homework Statement Suppose we have a potential such that $$ V = \left\{ \! \begin{aligned} 0 & \text{ if } x<0\\ \mathcal{E}x & \text{ if } x>0, x<L\\ \mathcal{E}L & \text{ if } x>L \end{aligned} \right. $$ for some electric field ##\mathcal{E}##. I'm trying to find the transmission...

Is it assumed that Hilbert space is an infinite manifold that the non-collapsing wave function occupies in Everettian QM? Thank you.

I am in high school and i am taking a independent research class that requires me to do a few months of research and then present it at a science fair. I have access to a good amount of materials. Nothing too complex because I'm in high school and there are limitations. Are there any ideas of...

Homework Statement I have a few questions I'd like to ask about this example. (C1 was already derived before the second part) 1. What does the line "The rest of the coefficients make up the difference" actually mean? 2. What does "As one might expect...because of the admixture of the...

I'm a newbie in all this, so I'm sure I'm wrong. :) There are several schools of thought about quantum mechanics: Copenhagen, many worlds, pilot wave,... etc.. They all have, as far as I know, in common the Schrodinger equation. And here I could be wrong in my assumption: It doesn't matter if...

When constructing a relativistic quantum mechanical equation, namely Dirac equation, what would happen if we choose the Hamiltonian so that it's not linear in the momentum operator and the rest energy? You could say, why don't try it yourself and see what happens? That's because my knowledge is...

Hi all, does anyone know if Bransden's book has a solutions manual out there somewhere? I would loathe to go through the chapters before realising that I can't find solutions to its exercises. If not, are there QM texts out there with a similar scope to this book that do have solutions manuals...

Hi I have heard that QM is the most accurate and scientifically tested theory to date. I have also read in many of these threads that it is silent when it comes to unobserved/unmeasured quantum systems? Is this not a contradiction in terms? I can say with almost 100% probability...

I am trying to understand what space is. Does QM state that Space is made of nothing? In other words it does not exist?

Shor's algorithm is rather the most interesting quantum algorithm as it shifts a problem which is believed to need exponential classical time, to polynomial time for quantum computer, additionally endangering asymmetric encryption like RSA and ECC. The real question is if there are other...

I was trying to help (elsewhere) a student with some QM related problem and I realized something. When discussing QM we underline the fact that electron doesn't behave as a particle, it behaves as a wave. Yet when we explain wave function we say something like "square of the wave function is a...

With E a,b = ( dλ ( a,a' b,b' λ) Suppose λ depends independently/locally on detector setting choices at A and B. For example suppose there are 360 detector settings at A and 360 at B , corresponding to 360 particle/detector interactions/outcomes at A = ± 1 and also at B = ± 1. Then as θ =...

I rather like Terry Tao, not only because he is Australian, a great mathematician, maybe even the greatest currently living, whose contributions range across a wide gamut of areas including QM (which interestingly he actually failed at university - but that is a story of bad study habits for...

Is the Entropic Uncertainty Principle taken seriously by experimental physicists? For example, is it considered more accurate than the HUP that uses standard deviations? Thanks in advance.

Hello! I am reading a derivation of the path formulation of QM and I am a bit confused. They first find a formula for the propagation between 2 points for an infinitesimal time ##\epsilon##. Then, they take a time interval T (not infinitesimal) and define ##\epsilon=\frac{T}{n}##. Then they sum...

I think he's pretty much nailed the relativity, QM and BTSM forums: https://xkcd.com/1861/ or https://m.xkcd.com/1861/ for mobile users.

First, if you want to refer to the Schrodinger Equation only.. is it only called Quantum Mechanics? Or does the word Quantum Mechanics also include Quantum Field Theory? If true. Then what words should you refer to the non-relativistic Schrodinger Equations only? About the forces of nature. The...

Hi, people I wondered if as prerequisites for QM, the Kreyszig (for func. analysis) and Hassani's book they be suffices .. Thank you in advance !

Hello everyone ! I would like to know if prob. theory is critical to learning Qm !

Please list all the practical applications of QM and QFT the way you know from memory.. so far the following is what I know. Practical applications of QM: 1. Understanding the double slit experiment 2. What else? Please enumerate Practical applications of QFT: 1. Solving for the Magnetic...

<Moderator's note: two essentially very similar threads merged.> Hello! I am a bit confused about the idea of measurement in QM. As far as I understand, if you measure the position of a particle, the wavefunction of that particle changes into a delta function, and thus the particle gets...

In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation? Could you tell me whether following is true...

Hello! I have a proof in my QM book that: ##\left<r|e^{-iHt}|r'\right> = \sum_j e^{-iHt} u_j(r)u_j^*(r')##, where, for a wavefunction ##\psi(r,t)##, ##u_j## 's are the orthonormal eigenfunctions of the Hamiltonian and ##|r>## is the coordinate space representation of ##\psi##. I am not sure I...

Homework Statement In the Griffiths book <Introduction to QM>, Section 2.3.2: Analytic method (for The harmonic oscillator), there is an equation (##\xi## is very large) $$h(\xi)\approx C\sum\frac{1}{(j/2)!}\xi^{j}\approx C\sum\frac{1}{(j)!}\xi^{2j}\approx Ce^{\xi^{2}}.$$ How to understand the...

I joined this site because I had questions and wanted to discuss topics on the subject of black holes. Lenny Susskind's lecture of this topic raised quite a few question a and ideas in my mind. I did write my concerns in the comments for the video, but I'll just paste that here as well. Here's...

Quote lifted from a thread in the cosmology forum. What does it mean to know the exact state of a QM system? QM predicts probabilities that particles will be in one of multiple states when the particles are observed, and when observed, not all properties of a particle are simultaneously...

This might become a series of questions, but let me begin with the most essential one. According to QM/QFT, would it be true that there is a non-zero chance for an object on Earth to instantaneously tunnel to the moon for example? Like let's say a paper with a note on it. Could this paper...

using the references below, the effective charge and the potentials are derived for either r >> 1/m or r << 1/m, so what happens between these two distances. Thanks https://en.wikipedia.org/wiki/Vacuum_polarization https://en.wikipedia.org/wiki/Uehling_potential...

Homework Statement I am not sure about (c) and (d). Firstly, I calculated the eigenvector of A : |v_1> = ( |2 > - |1> )/ √(2) ,eigenvalue -2 |v_2> = ( |2> + |1>) / √(2) , eigenvalue 2 For (c), basically it follows from part (b) where the probability of a_1 is given by the formula | <v_1 | ψ...

Quantum interpretations is the most controversial aspect of quantum mechanics (QM). Many feel that such controversial stuff should not be thought in general QM textbooks. Nevertheless, a large number of general QM textbooks contain relatively large sections or chapters on such controversial...

When I took undergrad QM, our last assignment was solving the 4 particle system as a function of inter-nuclear separation. I just read Shankar (30 years later) for a review. There was no mention of SCF theory in the book. Was my instructor ahead of the curve?

Could someone provide a good explanation as to why light's frequency doesn't change under refraction? The textbook I'm using gave us a two step derivation and I don't really feel like it did a proper job in explaining anything (it's Haliday). Also, a slightly *crackpot* follow up question -...

Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread...

I understand there exists some way of teaching QM via postulating commutation relation between coordinate and momentum operator. May be even not simply postulating but bringing some reasons why such a commutator should be equal to "i"? Could you recommend some good book or article which teaches...

Im very misinformed on this,and I was struggling whether to put this in the Quantum section,or Relativity.Please don't use advanced mathematics,and put everything into simple words for me,I can understand a bit of physics vocabulary so that is okay.

Suppose there are two independent experiments taking place \left\vert \Phi\right\rangle =\alpha _{1}\left\vert \phi _{1}\right\rangle +\beta_{1}\left\vert \phi _{2}\right\rangle and \left\vert \Psi \right\rangle=\alpha _{2}\left\vert \psi _{1}\right\rangle +\beta _{2}\left\vert...

Is the fact that QM uses complex numbers should be considered as a math artefact (as it is the case when complex numbers are used for alternate current circuit analysis), or, alternatively, it has some deep and important relation to the nature (or at least to the nature of the quantum theory)...

This is an interesting QM video. It would be interesting to get opinions about it from the QM students and experts alike.

Does anyone know of a good library in javascript that would help to develop technically accurate animations? I know there is stuff in python, but I'd like things to happen in the browser. Apart from linear algebra with complex valued matrices and vectors, I'd like to have things like numerical...

Is there a possibility that none of the current interpretations of QM are right? Or is the current interpretations all that there will be on the table?

Heads up, I only recently got into quantum mechanics and don't feel like I got a solid grasp on the material yet. 1. Homework Statement Given is the wave function of a free particle in one dimension: \begin{equation} \psi(x,0) = \left( \frac{2}{\pi a^2} \right)^{1/4} e^{i k_0 x} e^{-x^2/a^2}...

I have a few questions about interpretations that use retrocausality. I only know of 2. 1. TIQM - Transactional Interpretation of QM by John Cramer 1986 https://en.wikipedia.org/wiki/Transactional_interpretation 2. TSQM - Time Symmetric QM by Huw Price...

A paradigm shift for me occurred when, I now realize, that position and momentum are random variables in QM. As such, it does not make any sense to say things like "take the derivative of the position with respect time". Instead QM has the position and momentum operators which operate on the...

I'm trying to use the Animate function on Mathematica to show a gaussian wave packet passing through a delta potential. I'm quite new to Mathematica and this is by far the hardest thing I've had to do so please bear with me. I effectively want to solve the integral: ## \phi_k(x) = \left\{...

In Dirac’s QM book, Revised Fourth Edition (~1967), Chapter XI Relativistic Theory of the Electron, page 262, he reaches the conclusion that “…a measurement of a component of the velocity of a free electron is certain to lead to the result ±c.” Is this still the current thinking? (He is talking...

Homework Statement So we have a two state system, with unperturbed eigenstates ## |\phi_{1}\rangle##, ## |\phi_{2}\rangle ##, and Hamiltonian ## \mathbf{\hat{H_{0}}}## - i.e ##\mathbf{\hat{H_{0}}}|\phi_{1}\rangle = E_{1}|\phi_{1}\rangle## We shine some z-polarized light on the system. This...

Are interpretations that are non linear with respect to the wave function (eg. GRW, transactional) compatible with string theory?