Qm Definition and 1000 Threads

Hello all, I would like some guidance on how to approach/solve the following QM problem. My thinking is that Fermi's Golden Rule would be used to find the transitional probability. I write down that the time-dependent wavefunction for the free particle is...

hello matrix and wave formulation of QM are equivalent theories i.e they yield the same results Which one is most frequentely used by professional scientists in solving real problems and why ?

Here's the question ^ My first thought to solving this is to use Heisenberg's uncertainty principle. $$\Delta x \Delta p = \frac{h}{4\pi}$$ Now, we approximate ##\Delta x = \frac{L}{2}##. Then, plug and chug we end up with:$$p =\frac{h}{2\pi L}$$ I thought this was it, especially because this...

Here we are talking about non-relativistic quantum physics. So we all know kinetic energy T = E - V = \frac{1}{2}mv^2 in classical physics. Here V is the potential energy of the particle and E is the total energy. Now what I am seeing is that this exact same relation is being used in quantum...

Hello! I am dealing with a problem of a 2 level system (an ion in my case) placed in a Penning trap. Basically the ion is moving inside the trap under the influence of the magnetic and electric field and I need to study its inner 2 level system (basically the lowest 2 energy states) while it is...

I have one request, I hope you could answer it…. I saw this article that makes heavy assumptions based on Quantum Electrodynamics, like something like formation of an energy domain or sorts, and it connects it with brain activity which is super weird, I did ask a neuroscientist and he said he...

A recent thread by @coolcantalope was accidentally deleted by a Mentor (I won't say which one...), so to restore it we had to use the cached version from Yahoo.com. Below are the posts and replies from that thread. The cached 2-page thread can be found by searching on the thread title, and is...

Does mean velocity of particle equal group velocity of wave packet in QM?If they do not equal which of them is classical velocity?

https://www.scientificamerican.com/article/new-views-of-quantum-jumps-challenge-core-tenets-of-physics/?fbclid=IwAR0z2pTmGqTBkm2JzvSNe6piKPZCGbhdpyZWcHeLO_2B-w5fPxFRKgfrGvY I love quantum physics almost mystical and paradoxical nature. That seems to be ending. Especially with the advent of...

I hope my thread won't be closed (too soon) and some forummers can shed their light over my question. Let's suppose a deterministic universe. I assume all events have a cause, that everything is cause and effect. Then, given that the state of the universe at some instant is X, and this leads to...

In classical probability theory, a probability space has a set of "point" or "outcomes" which may be multidimensional vectors. "Events" are sets of these points. By analogy, in QM, it seems a macroscopic event would defined (in principle and mathematically) by as a set of possible...

In one of the Insights. Either QM is incomplete (because we only have access to probabilities in conventional experiment) or there are Many Worlds. I want to pick incompleteness. But in Einstein context of it. Incompleteness means there were hidden variables. Is there another meaning of...

Will brain-computer interfaces that are hooked up to quantum measurement devices reveal more about quantum mechanics?

[Moderator's note: Thread spun off from previous discussion as it is more technical.] Adding to this: the formalism of QM is quite flexible when it comes to applying the projection postulate. We can even apply it before the time of measurement. Consider a preparation (at time ##t_0##) of a...

In the 3rd edition of the Introduction to Quantum Mechanics textbook by Griffiths, he normally does the notation of the expectation value as <x> for example. But, in Chapter 3 when he derives the uncertainity principle, he keeps the operator notation in the expectation value. See the pasted...

Hello,everyone. Which material is best for Nelson's stochastic interpretation of quantum mechanics?

Hi PF, A(x,t) is the probability amplitude at time t that a particle is at x. If it was emitted at (0,0) the propagator gives its value. I wonder if QM can give the amplitude of time probability B(y,t) that an impact will occur (for a given y) at any t. consider a screen behind the two slits, it...

By definition , ##\ket{+x} = \alpha \ket{+z} + \beta \ket{-z}.## Therefore we proceed , \begin{align*} \langle S_{x} \rangle &= \lvert \alpha \rvert^{2} \left(\frac{\hbar}{2}\right) + \lvert \beta\rvert^{2} \left(-\frac{\hbar}{2}\right) = (\alpha^{2} - \beta^{2})\left(\frac{\hbar}{2}\right).\\...

Here is the article: https://www.sciencemagazinedigital.org/sciencemagazine/21_august_2020/MobilePagedArticle.action?articleId=1611119#articleId1611119 If 2 experimenters (or people) cannot agree on a single observation does this mean that science which depends on many observers agreeing on...

Hello! I was wondering if there'd be any problems using another QM book (like Shankar, Ballentine etc) in a course where the standard literature is Griffiths Introduction to Quantum Mechanics? By that I mean is there ever any disadvantages to going to a more advanced textbook (assuming you...

In QM, matter is made of standing waves (The postulate of QM and the Schrödinger Equations). The momentum of matter is related to the wavenumber (de Broglie wave). The electromagnetic waves are the traveling waves (Electrical Engineering). Can we expand the hierarchy of waves to the vacuum - a...

First of all, I got to decide what I'm going to use to make the simulation. I know Fortran, Matlab etc but I'm pretty sure these won't help me much. I learned some C++ a couple years ago but my knowledge is rusty, however I think I'm going to use that combined with Unreal Engine, since it makes...

In many physics curricula, some elements of the so called "old" (Bohr-Sommerfeld) QM are taught before teaching the actual QM. The pedagogic value of such teaching may be doubtful, but for someone without prior knowledge of QM, the old QM is more intuitive than the actual QM. That's because the...

Having discussed interpretations of QM here and elsewhere, to only a basic level, I have encountered proponents of what is described as "anti-realism". This is not to be confused with "non-realism", which might be equated with simple instrumentalism or "shut up and calculate". To try and...

I have a (trivial) question regarding summation notation in Quantum mechanics. Does ∑cnexp(iknx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e. n ∞ ∑exp(iknx) -∞ I believe it does to be consistent with the Fourier series in terms of complex exponentials...

Hi All Have a look at the following discussion about QM: Its long so I do not expect too many people to watch it in its entirety. But it does show confusion about QM even amongst educated people, and the physicist involved IMHO seemed a bit 'confused' himself. You can easily see how the...

The Penrose interpretation postulates that the wave function is real and that there is objective collapse without departing from reality as we know it. It does not make any assumptions; the observations of quantum mechanics and classical mechanics are exactly what they appear to us. "Accepting...

Hello! This questions might not make sense and I am sorry if that is the case (I am asking from a QM class perspective). I am a bit confused about the idea of spontaneously symmetry breaking (SSB), from the point of view of QM. I am talking here about the energy plot looking like a mexican hat...

I was over on another forum discussing what Einstein thought of QM - namely he thought QM correct - but incomplete. His viewed changed a bit over time, but that was his final view. Anyway here is the reply I got: No serious Physicist (including all of my professors) thinks he was right. It's...

Hello, I want to try studying QM. I have already read Susskind Minimum QM. Now I have some trouble focussing while reading and mild dyslexia. So I only want to read the stuff I need (doesn't everyone?). HOW do I find the right sequence of the right books to progress from basic to more...

I was originally going to start a thread on individual interpretations of quantum mechanics to try to understand them better, but after reading this article by @PeterDonis it might make more sense to use that as a starting point and try to understand how the different interpretations fit into...

I'm diving into the RQM and one thing still puzzles me. I have hard time understanding this: Taking the model system discussed above, if O′ has full information on the S+O system, it will know the Hamiltonians of both S and O, including the interaction Hamiltonian. Thus, the system will evolve...

I was thinking that QM and QM practicioners tend to stay away from the ontology part of QM, and see the QM framework as useful for predicting measurement outcomes. But if I see the properties of wood or plastic, they are explained by the properties of the particles they are "made up from", and I...

I write this post because there are some people that get irritated by my posts. I get why you do. I think the signal I am getting in several threads of mine, is that you could try to understand QM through interpretations, but that the prerequisite is that you then also have to understand the...

Apologies in advance for my ignorance, I don't really have a reference to consult and Google hasn't been too helpful! In standard probability theory there are a few common useful formulae, e.g. for two events ##S## and ##T## $$P(S\cup T) = P(S) + P(T) - P(S\cap T)$$ $$P(S \cap T) = P(S) \times...

Hi, I think I'm having a bit of a brain fart...I'm messing with this numerical code trying to understand the 1-D time-independent Schrodinger's equation infinite square well problem (V(x) infinite at the boundaries, 0 everywhere else). If normalized Phi squared is the probability of finding...

Hi, so I'm having trouble with a homework problem where it asks me to find the number of states with an energy less than some given E. From this, I was able to work out the energy E to be $$ E = \frac{\hbar^2}{2m} \frac{\pi^2}{a^2} \left( n_x^2 + n_y^2 + n_z^2 \right) $$ and...

Applying the time reversal operator to the plane wave equation: Ψ = exp [i (kx - Et)] T[Ψ ] = T{exp [i (kx - Et)]} = exp [i (kx + Et)] This looks straightforward as I have simply applied the 'relevant equation' however my doubt is in relation to the possible action of operator T on the i...

I was wondering this question for quite some time because this view seems to work surprisingly well and also coincides with how the state space must be setup in any attempt model QM within classical probability theory. So starting with the hydrodynamic formulation from...

I was learning about Degenerate Perturbation Theory and I encountered the term 'Degenerate Subspace', I didn't really understand what it meant so I came here to ask - what does it mean? will it matter if i'll say 'Degenerate space' instead of 'Degenerate Subspace'? and subspace of what? (...

I think it can do more than the wave only events we know of (superposition, entanglement, and tunneling). If the quantum field doesn't care about spatial distance, does that mean every unobserved quantum wave is already everywhere throughout the quantum field? Does it explain spooky action at a...

Where can I learn more about this conception of reality?

I am very interested in the philosophy and science of the mind, as well as consciousness in neuroscience. I am also very interested in QM. Now, I wonder how QM can be potentially connected to my two previous interests on the consciousness and mind. I would also appreciate any reference to...

Summary:: I am a last year high school student. I haven't chosed physics for my course, but I am very interested in QM, because I believe it act lik a gateway to the meaning of existence, and so the nature of mind, my particular interest. I want to know which textbook is the best for me. I am...

Check it out: https://www.amazon.com/dp/B07PYMLZWJ/?tag=pfamazon01-20 Its available free if you have Kindle Unlimited. Many books do not get right that Einstein knew QM very well indeed and greatly admired Dirac, of whom he said: 'Dirac, to whom, in my opinion, we owe the most perfect...

I have a simple question as a layman in the field: Is this worth reading, and even more, is it a contribution to possibly shorten the endless discussions in this subforum? https://www.nature.com/articles/s41598-019-56357-3.pdf

If I understand this question correctly, I am supposed to prove an integrate from negative infinity to infinity ∫x|∅(x)|2(1+|x|)ndx is finite. Sorry, but I have no idea.

Personally I tend to believe all (or almost all) of the interpretations of QM are unsatisfactory simply because they tell us something that we already know but do not tell us something we don't know. That is, they do not predict new phenomena or principles or properties of matter, etc. that can...

In quantum mechanics, the Eigenfunction resulting from the Hamiltonian of a free particle in 1D system is $$ \phi = \frac{e^{ikx} }{\sqrt{2\pi} } $$ We know that a function $$ f(x) $$ belongs to Hilbert space if it satisfies $$ \int_{-\infty}^{+\infty} |f(x)|^2 dx < \infty $$ But since the...

It seems that with every discussion I engage in, new thoughts and questions about QM keep popping up. I'm sure this is pretty standard but I hope that my questions haven't crossed the line into being excessive. I know that in the EPR paper the authors set out a criterion that, if fulfilled...