Quantum mechanics Definition and 994 Threads

https://www.nature.com/articles/s41598-019-43323-2. Please note Figure 4 p.4 of the article, and the following description: " In Fig. 4(h), the right slit is completely blocked, the interference fringes have disappeared completely and only the diffraction image of the open left slit remains."...

so I thought that when a system was measured there could be an interaction between the measurement device or environment and the system but overall energy was conserved, but I came across these 2 articles which seem to imply this is not the case...

I will include a photo. Essentially, we need to prove that dp/dt + the gradient of J(x,t) = 0. We are getting that the two are instead equal and opposite, and have checked with multiple people.

I'm trying to repair the dismal state of my knowledge of QM, so I downloaded Tong's notes and have read through them a couple of times and I have a question. Tong says (section 1.1.1, p7 in the pdf) that an overall constant phase factor ##e^{i\alpha}## infront of a wavefunction describes an...

Among the most well-known interpretations of Quantum Mechanics is that of the "Many Worlds," in which all possible outcomes of a measured quantum event occur simultaneously in some alternative universe. Now, I realize there is some manner of debate as to whether or not the different...

TL;DR Summary: Is "Quantum Mechanics Demystified" a good book for a beginner for self-studying? I'm a layman with background in high school physics and undergrad calculus. Is "Quantum Mechanics Demystified" by David McMahon a good book for self-studying and learning quantum mechanics?

I think that the lore on the need of having probability interference in quantum mechanics and then a complex probability originates in Feynman interpretation of space-time paths, whose probability is weighed with a complex exponential that approaches a dirac delta. But I can not pinpoint a...

I would like to ask what the current scientific understanding on the abilities of various types of polarizers to affect the wavefunctions of particles is. Its based on an earlier thread OP of mine and one of the replies in the thread. So the Born rule is pretty fundamental to quantum mechanics...

I just watched Sabine's Hossenfelder very recent new video on the Quantum Cheshire effect. From experience, everything Sabine's says on either entanglement/quantum interpretations or not-physics, is heavily biased to her worldview. However I thought it was fun to see what she was going to say...

In the article “Quantum mechanical measurement in monistic systems theory” doi:10.23756/sp.v11i2.1350 there is no collapse of the wave function and only one world. Can wave particle dualism be replaced by a monistic model?

I have this following Gaussian wavefunction. I found the constant C to be $$\sqrt{\sqrt{\frac{2 \alpha}{\pi}}}$$. Now they're asking me to find the normalized impuls wavefunction $$\phi(p)$$. I tried to use the fourier transform relation $$\phi (p) = \int e^{-\frac{i ( p x)}{\hbar}} \Psi...

I recently watched "A New Approach to Quantum Mechanics" by Dr. Yakir Aharonov Part 1 (12.12.2023 | Institute for Quantum Studies) on YouTube (and also Part 2 and 3). I was naive enough to believe it was really new. Only when I searched for a valid reference in order to be allowed to ask about...

Could you please suggest a good textbook for self-studying quantum mechanics? Not something too advanced. I have a math degree, so I'm not averse to equations.

Happy new year to all the forumers. The Wigner's friend paradox appeared in the early years of quantum mechanics: Wigner knows that his friend looked inside the box to see if the cat is dead or alive. He has two cells in his mind to put what his friend saw. As he ignores the result, he may...

I have been interested in physics for a very long time. Initially in high school celestial mechanics and soon afterwards quantum mechanics. During my chemistry studies I specialized in quantum chemistry at the end of my bachelor and continued to do a Bachelor and Master in pure Mathematics, with...

I have this 1D LHO problem. https://gyazo.com/4cd913d9da3a743443ef7dc2d1c2ab1e For ##\psi_n (x)## I get $$\left( \frac{\alpha}{\sqrt{\pi} 2^n n!} \right) ^{\frac{1}{2}} e^{\frac{- \alpha^2 x^2}{2}} H_n(x)$$ with ##E_n = (n+ \frac{1}{2}) \hat{h} \omega##. where ##\hat{h}## is hbar. For...

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I study QM, in particular I need to implemend the computation of vibrational spectrum for polyatomic molecules by forca constants in the "rigid rotor - harmonic oscillator" approximation in my program Chemcraft. I have watched some videos from the channel "Professor Dave explains". The...

I desperately need a good resource for quantum mechanics. This semester, our lectures have been absolutely terrible. Though I managed to avoid this by studying hard, the lectures and notes were so critically inadequate that most students (not including me) used ChatGPT to complete any online...

I want to verify some inspection I'm making at this problem. Because of the infinite barrier at ##x=0##, we expect the wave function to take the value 0 there to preserve continuity. As such, we can make the conclusion that the wave function will just be a sine term in the [0,a] region. But...

Hello, I am following the paper: https://www.yumpu.com/en/document/read/42212557/exact-exchange-in-density-functional-calculations and I am confused on page 14 where the generalized Kohn-Sham equations are derived. I follow that the ground state energy is The minimization of this step leads...

Dear friends please help me, for I am completely confused and can not understand the logical connection between two postulates of quantum mechanics. One postulate states, that if some observable is being measured, for instance coordinate, then the superposition of many possible states, which...

I was revisiting @DrChinese 's Bell's Theorem with Easy Math which sparked a few questions, which I am hoping might offer a potential path to a deeper understanding of Bell's Theorem and Quantum Mechanics (QM) in general. The explanation uses light polarisation experiments to explain how we...

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...