Quantum mechanics Definition and 994 Threads

Absolutely no clue on how to even begin this question due to the exceptionally poor quality of our lectures, who has also flatly refused to give out any solutions, which I could have used to understand what is going on. I assume the energy has to be obtained by using the eigenfunction equation...

I hold a PhD in physics and am very interested in education. I have been a high school math teacher, teaching assistant (both graduate and undergraduate, physics and chemistry), and tutor.

I don't get the step from (3-22) to (3-23), can you how this integral was calculated? Thanks! Below there is a screenshoot of (3-9). Images are taken from "Intermediate Quantum Mechanics, 3rd Edition - Bethe, Jackiw".

In Feynman's famous Physics book, in a discussion of the generality of Maxwell's equations in the static case, in which he addresses the problem of whether they are an approximation of a deeper mechanism that follows other equations or not, he says: I was wondering first of all if this was a...

Not really even sure how to approach this problem , I would guess if we need scalar answer we would need to combine these two given equations together but I'm unfamiliar with such methods, in the book there is methods to make a ket to a bra and then matrix part transposes and multiplies with the...

TL;DR Summary: Quantum mechanical calculations are complex and the number of people capable of performing them is limited. In this thread, rough estimates are requested for the number of people that perform quantum mechanical calculations. Please estimate - somehow - the number of people that...

At low photon energies, the probability of the photoelectric effect to occur increases, but the probability of the photoelectric effect to happen also increases when going towards most inner shells like K shell but inner shells require much more photon energies to be broken, so isn't there a...

How does a photon interact with EM field of a nucleus thus exchange momentum and recoil the nucleus when pair production happens?

I wish you well. I am interested in quantum mechanics.

Hi, I am new here so apologies if i am not using the right subforum. I don't have a physics background so i am not very technical but i do have a little bit of understanding. I was reading this paper by hawking/hertog and came across something that ended up confusing me. Here is it: "Pre-big...

$$\newcommand{\bra}[1]{\left \langle #1 \right \rvert} \newcommand{\braxket}[3]{\left \langle #1 \middle \rvert #2 \middle \rvert #3 \right \rangle} \newcommand{\ket}[1]{\left \rvert #1 \right \rangle} \newcommand{\expec}[1]{\langle #1 \rangle}$$ Ballentine asks us the question at the end of...

Niels Bohr famously said --and I paraphrase-- that QM is an abstract description of nature and that it can only prescribe what we can say about nature rather than what nature is. What does QM say about the movement of a particle? Is this movement positively ascertained to be smooth and...

Ballentine, in his Chapter 8.1, appears to give the attached recipe for *in principle* preparing an (almost) arbitrary (pure) state (of a particle with no internal degrees of freedom) by the method of "waiting for decay to the energy ground state". My questions are fourfold: 1) From (8.1), we...

I am struggling with the latter, and think that I somehow need to assume ##f## is real-valued to proceed? My work: The position distributions are equal since $$P_{-m}(\mathbf{x}) = |\Psi_{-m}(\mathbf{x})|^2 = |f(r)Y_l^{-m}(\theta,\phi)|^2 = |f(r)(-1)^m(Y_l^{m})^*|^2 =...

Dear PFer's, this is a problem I have been struggling with for years. Is energy conserved (not in a statistical sense) in QM? The so-called collapse of the wavefunction, occurring during a measurement process, is incompatible with energy conservation - at least in the general case. A starting...

Thermodynamics deal with quantum mechanics all the time, so I wondered what role it played in a internal combustion engine. Could we calculate it and how does it affect the engine's final output?

Hi, everyone. Please check the following questions (extracted of the cohen Tanpoudji) for the first question, here my Hamiltonian operator. It's easy to see that it commutes with Lz and Pz. Now we can determine a common eigenvector basis for these 3 operators. For the angular part we need to...

How to prove that the tensor product of two same-dimensional Hilbert spaces is also a Hilbert space? I understand that I need to prove the Cauchy Completeness of the new Hilbert space. I am stuck in the middle.

TL;DR Summary: How to learn about the Hydrogen Atom from Level 2 OU Degree I am copleting the second year of the OU physics degree and "understand" what is taught about the Hydrogen atom there, energy levels et al. I am not yet competent in calculus here. I seek a means, buy a book....view...

Hi. I am not being able to understand how we are getting the following spectral decomposition. It would be great if someone can explain it to me. Thank you in advance.

Hi. This is Annwoy Roy Choudhury. I have just completed my first-year undergraduate studies in Physics. I am new to Quantum Mechanics. There are certain confusions I have regarding Quantum Measurements. It would be really kind of you to help me out. Postulate 3 states, An example is, Let's...

Confronted with my inability to grasp Witten's Susy QM examples of supersymmetry breaking, I concluded that the problem was that I was not understanding spontaneous symmetry breaking in simpler contexts. It seems that SSB is not possible in QM because of tunneling between the different states...

How is the Schrondinger equation related to the Heisenberg equation?

Hi, I have problems with the task part b and g To solve the task, we have received the following information Task b First, I wrote down what the state ##\psi## looks like $$\psi=\frac{1}{\sqrt{N}} \sum\limits_{k}^{} \psi_k$$ $$\psi=\frac{1}{\sqrt{N}} \sum\limits_{k}^{} \frac{1}{\sqrt{N}}...

Hello! I was recently listening to StarTalk podcast and (re)learned that the electron is one of the most elusive particles for which there is no known size. Have there ever been any attempts to measure the size of the electron, either directly or indirectly, from either a practical or theory? I...

I just finished an online YouTube Quantum Mechanics course by Frederic Schuller. The course was in two parts, the one Schuller was doing was theory; it was an approach I had been trying to develop myself and had never found anywhere. I don't know what exactly to call the course label: it was...

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...