Quantum mechanics Definition and 994 Threads

I'm given the wavefunction and I need to find the normalization constant A. I believe that means to solve the integral The question does give some standard results for the Gaussian function, also multiplied by x to some different powers in the integrand, but I can't seem to get it into...

I keep coming across this descriptor, "two (or three) independent, non-interacting parts," in many books on QM (for example, Penrose's Shadows of the Mind). It is usually followed by a mathematical description (for example, state vector |A>|B>). I can wrap my mind around the quantum paradox of...

Hi. Question as in the summary. Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum. What do you need to establish that spin is a conserved quantity? I'm finding references to situations where spin is not a...

As you may have noticed, I am obsessed with understanding the difference between two views of quantum mechanics, one of which can be called the "standard" view, and the other the "realist" view. The difference, of course, is very complicated, but I believe that the essence and origin of the...

In interpretations of quantum mechanics there are two types of physicists: those who care about ontology and those who don't. The ontologists, or realists, want to know what is the world made of. The non-realists, on the other hand, think that this question is not relevant to physics. Usually...

Is Quantum Mechanics a Probabilistic Forecast of nature?Someone I know told me their interpretation of QM is that QM only a probabilistic forecast of systems like electrons around atoms. I would like someone to analyse this interpretation and say if its valid or not. According to this person we...

Hello, As a layman in physics, I wonder the ideas of people who have more knowledge in physics than I do about the theories of Swiss Physicist Nicolas Gisin and his arguments about the intuitionist mathematics. Is there a way to reconcile these ideas with more fundamental theories like SR and...

For two quantum oscillators, I have raising and lowering operators and , and the number operator . I need to check if operators below follow commutation relations. Now as far as I know, SU(2) algebra commutation relation is [T_1, T_2] = i ε^ijk T_3. So, should I just get T_1 and T_2 in...

Was trying to understand the inequality test. The only article ever that I've found that explains it simply is the 1981 article, Bringing home the atomic world: Quantum Mysteries For Anybody. All other explanations require trust and understanding of polarisation, which is a huge deal. So i now...

Hi. I looked everywhere for a specific book but I cannot find any pdf copy of it. The book specifics are below: Publication Name: Principles of Quantum Mechanics Author: Hans C. Ohanian Publisher: Benjamin Cummings Publishing Company ISBN-10: 0137127952 ISBN-13L 9780137127955 I would...

There is a question that puzzle me when I apply numerical method to principal value integral. Let me descibe it. We make use of the fact that the integral ##\int_0^\infty \frac{dk}{k^2-k_0^2}## vanishes, namely, $$ \int_0^\infty \frac{dk}{k^2-k_0^2} = 0 . $$ We use this formula to express a...

Hi, I would like to know why a particle with spin=0 can't posses a magnetic dipole moment? Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}## It seems like the right hand side is the magnetic dipole...

Hi, Given a spin in the state ##|z + \rangle##, i.e., pointing up along the z-axis what are the probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##? My problem is that I'm not sure to understand the statement. It seems like I have to find the probabilities of measuring an eigenvalue...

I am following [this YouTube lecture by Schuller][1] where he finds the appropriate formalism for the quantum mechanics in the physical curved space. Everything makes sense to me but at the very end I see that we find the pull backed connection one-form on the base manifold. He says to the end...

Starting from the Heisenberg equation of motion, we have $$ih \frac{\partial p}{\partial t} = [p, H]$$ which simplifies to $$ih \frac{\partial p}{\partial t} = -ih\frac{\partial V}{\partial x}$$ but this just results in ## \frac{\partial p}{\partial t} = -ih\frac{\partial V}{\partial x}## and...

Hi everybody. Some years ago I came across a video on youtube where they talked about an experiment with small and large envelops, when the small ones were placed into the large ones and then it resulted in something interesting. It might have been an instance of delayed choice, but I am not...

It this correct explanation why quantum is not valid for large object? Why would small object want to hide their information?

It is often argued that Dirac Equation is not valid as relativistic quantum mechanics requires the creation of antiparticles. But, there are also some arguments that suggest otherwise. For example, I saw Arnold Neumaier's website on this that there are multiparticle relativistic quantum...

Hello, I hope you are doing well. I had a question about the eigenvalue problem of quantum mechanics. In a past class, I remember it was strongly emphasized that the eigenvalues of an eigenvalue problem is what we measure in the laboratory. ##A\psi = a\psi## where A would be the operator...

Hi, I'm not sure to understand what ##| \phi_n \rangle = \sum_i \alpha_i |\psi_n^i## means exactly or how we get it. From the statement, I understand that ##[U,H] = 0## and ##H|\psi_n \rangle = E_n|\psi_n \rangle## Also, a linear combination of all states is also an solution. If U commutes...

Sakurai, in ##\S## 5.7.3 Constant Perturbation mentions that the transition rate can be written in both ways: $$w_{i \to [n]} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \rho(E_n)$$ and $$w_{i \to n} = \frac{2 \pi}{\hbar} |V_{ni}|^2 \delta(E_n - E_i)$$ where it must be understood that this expression is...

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.

Hi, While studying the spin 1/2, I'm facing some confusions about the spinors and the eigenspinors. I understand that ##\chi = \begin{bmatrix}a \\ b \end{bmatrix}## is the spinor with ##\chi_+ = \begin{bmatrix}1 \\ 0 \end{bmatrix}## and ##\chi_-= \begin{bmatrix}0 \\ 1 \end{bmatrix}## the...

The titular paper can be found here, https://doi.org/10.1088/1751-8121/ac6f2f, and on arXiv as https://arxiv.org/abs/2101.10931 (which is paginated differently, but the text and equation and section numbers are the same). Please see the abstract, but in part this 24 page paper argues that we...

So, in a rare instance I actually read APS News, I came across “New Experiment Suggests Imaginary Numbers Must be Part of Real Quantum Physics.” In November 2022, Volume 31, Number 10. Since complex numbers are isomorphic to a real 2x2 matrix algebra, I was confused how such a claim can be...

Hi, I'm working on a problem where I need to find the different energies allowed for a potential, and I found this link https://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html, which is similar of what I'm doing. I'm using mathematica to find the values of E. However, I'm not sure how...

Is the answer 0.748?

Hi I’m looking for a textbook that shows the derivations of equations such as the different forms of the schrodinger equation fully and step by step.

I have no idea where to start with this problem. I am interested in any hints, or ways to proof this. But i would especially like to know how the commutator is connected to the identity.

I was not able to attempt since I don't know which formula or method can be used to solve the problem

Alain Aspect, John Clauser & Anton Zeilinger have rightfully received the Nobel prize for their contributions to quantum information, as they were three of the main pioneers of quantum information. However, is it now impossible or very unlikely that other physicists working on this field (e.g...

The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem: 1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...

I have made solutions a-d, but my fermi velocity seems too big.

Hi, I have hard time to really understand what's a stationary state for a wave function. I know in a stationary state all observables are independent of time, but is the energy fix? Is the particle has some momentum? If a wave function oscillates between multiple energies does it means that the...

I found a paper (https://arxiv.org/pdf/astro-ph/0411299.pdf) which talks about quantum systems emitting energy due to spacetime expansion. Is this true or only a hypothesis?

I read in the following book A history of the sciences by Stephen F. Mason. About the discovery of the electron the write what I attached in the picture. I wonder what do these positive rays traveling in the opposite direction they talk about consist of? Some ions or what? I understand that the...

Hello guys, I don't know if this is the right place to ask, so please be kind :/ I have a question regarding the location of an electron that belongs to an atom. A teacher told me that the probability of an electron to be found within its orbital is around 99%. When I asked about the remaining...

In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is...

What is it of the photon that gets polarized from a quantum mechanical perspective? In the classical perspective it is often thought that it is the oscillating electric field that gets polarized. But in the quantum case: Is it the de Broglie wave function? Or is it the spin and in case it is the...

I am reading this chapter 3 from the book called The Quantum Vacuum by P.Milonni.(Attached in the pdf, look at chapter 3.2 Spontaneous emission)There they say that spontaneous emission is due to both quantum fluctuations and radiation reaction. They say the transitions induced by the quantum...

Hello, I'm hoping someone can help me understand a statement in Sakurai Modern Quantum Mechanics (3rd edition). In particular, in the section that describes free particle in infinite spherical well (page 198, section 3.7.2), after the text has shown that for a given ##l## value, the energy...

I have found J^2 and Jz, but I am not sure how to find Jx and Jy. I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results. Thanks!

[Mentor Note -- thread moved from the schoolwork forums to the technical forums] Homework Statement:: Tentative Note and summary on the origin and the evolution of information in the universe. Relevant Equations:: none As a teacher of physics I got many questions asked by my students when...

So this expression is apparently in Sz basis? How can you see that? How would it look in Sy basis for example? The solution is following. They are putting Sz as a basis, bur how do you know that Sz is the basis here? Thanks

I can't figure out how they get i/sqrt(2) for normalisation of c1. Why is it a complex number? If I normalise c1 I just get 1/sqrt(2) because i disappears in the absolute value squared. Thanks

I'd like to understand how gravity does not combine with quantum mechanics. At least there is no accepted theory of quantum gravity, so I assume it is not solved? I'm only starting to learn QFT and eventually GR. Maybe, someone can already outline where those theories fail to combine and comment...

I have found an answer to all of them (a-e) but I don’t know how to plot the function. Thanks!

I am learning Dirac notations in intro to quantum mechanics. I don’t understand why the up arrow changes to down arrow inside the equation in c). My own calculation looks like this:

I have a lecture slide that shows how to find S_x and S_y. I get all the steps except the last row. Where did 1/2 come from? I think my linear algebra needs polishing. Thanks!

I'm wondering about some aspects about black holes (BH) and singularities, but since all my questions have to do mostly with quantum mechanics, I placed this thread in here. OK, let's assume there IS a singularity in the middle of a BH. A) Pauli exclusion principle (PEP) says no two fermions...