Quantum mechanics Definition and 994 Threads

I join as a 69 year old retired electrical engineer who is interested in physics. I have particular interest in particle physics and quantum mechanics. I don't expect to provide answers on this forum, but I do intend to ask questions.

We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...

In non relativistic quantum mechanics, the expectation value of an operator ##\hat{O}## in state ##\psi## is defined as $$<\psi |\hat{O}|\psi>=\int\psi^* \hat{O} \psi dx$$. Since the scalar product in relativistic quantum has been altered into $$|\psi|^2=i\int\left(\psi^*\frac{\partial...

Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$ Terms in...

Is there a view in quantummechanics, of quantummechanics, without time as a concept?

I heard something today about the "informational interpretation" of quantum mechanics and a phrase used was "it from bit." Is there actually such a thing? What does it mean, and how is it distinguished from other interpretations like MWI or Copenhagen?

Hello, I am trying to figure out the right way to approach this. First of all, other than the different Bohr radius value, does the change to a negative pion make any other difference to calculating the probability? Also what would be the correct way to apply the "small volume"? What I'm...

* The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is ##\vec{\mu} =g\frac{q}{2m}\vec{S}## * It's...

Hi Fellas! My first post after a long hiatus from forums. Feeling nostalgia (this is the place where it all began, my fuel for quantum fascination so to speak). I am revisiting the mathematical formulation of quantum mechanics with the dimensional (MLT) perspective. I want to understand what...

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Summary:: I am in the highest level Quantum class at my university- technically considered a grad class. I am an undergrad and need advice on just how to learn it. What study tips? Good Youtubers? Physical simulations? Anything that helped you in quantum mechanics. Hello! I am an undergrad...

Is Modern Quantum Mechanics, 3rd Edition, by J. J. Sakurai and Jim Napolitano a good book to learn quantum mechanics from?

According to the uncertainty principle, when we measure a micro-object with a measuring device, we cannot predict what value the device will show. But if we knew exactly the wave function of this device, together with the wave function of the micro-object, could we exactly predict the result of...

Hi! I want to self study some of quantum mechanics so i need introductory textbook. I've taken courses on linear algebra that covers all "Linear algebra done right" by Sheldon Axler, multivariable calculus, two courses on general physics and the basics of differentials equations. I really like...

Can you please suggest a good introductory statistical and quantum mechanics book which can be self studied. My math background : I've done multivariate calculus, vector calculus, linear algebra ,some complex analysis all at the usual undergraduate level. The books I've self studied thus far...

This is a surface level question and I don't want to go into detail. Imagine an algorithm which when used with a sensor output gives the statistical moments of a variable in nature (for example mean and standard deviation of a variable). The sensor measures this once in a while (like once in a...

Please be kind to help.I would be grateful

I recently started studying some quantum mechanics, so far I have been using online resources(like MIT OCW 8.04/8.05, and Tongs notes I think I have reached a stage where I understand the Schrodinger eqn and can solve it for various potentials(including for the H-atom) but I don't know anything...

"B0 is a static magnetic field (produced by a superconducting magnet) that initially causes the protons in the body to align with the field and precess at the larmor frequency along the z axis . From a mathematical perspective this precession around the B0 axis occurs due to the time evolution...

A lot of people say that Quantum Field theory (QFT) an Quantum Mechanics (QM) are equivalent. Yet, I've found others who dispute these claims. Among the counter-arguments (which I admittedly do not have the expertise to pick apart and check their validity in full) are the following: 1) While QFT...

I just finished a new paper, A. Neumaier, Quantum mechanics via quantum tomography, arXiv:2110.05294. (later renamed to) A. Neumaier, Quantum tomography explains quantum mechanics, arXiv:2110.05294. Abstract: Starting from first principles inspired by quantum tomography rather than Born's...

Hello all, So I've been working through the solutions to some simple introductory problems for the Schrodinger Equation like the infinite square well, and I'm trying to make sense of how to think about the phase component. For simplicity's sake, let's start off by assuming we've measured an...

Take a simple case: A system is prepared in state ##\rho_i## at time ##t_0##, and a projective measurement is performed at time ##t_2## with an outcome ##b##. We can retrodict a projective measurement outcome ##a## at time ##t_1## where ##t_0<t_1<t_2##$$p(a|b) =...

for undergraduate students how to explain this?

An axiomatization of classical mechanics such as the one by McKinsey et al. (1) does not contain any reference to humans or experiments, and does not contain the magic (irony!) words of quantum mechanics, i.e. observables and measurements. (1) McKINSEY, J. C. C., et al. “Axiomatic Foundations...

Now from the relevant equations, $$U(t) = \exp(-i \omega \sigma_1 t)$$ which is easy to compute provided the Hamiltonian is diagonalized. Writing ##\sigma_1## in its eigenbasis, we get $$\sigma_1 = \begin{pmatrix} 1 & 0\\ 0 & -1\\ \end{pmatrix} $$ and hence the unitary ##U(t)## becomes...

Summary:: The problem solutions contain a lot of unjustified steps, making them pointless. I am trying to use Griffiths Introduction to Quantum Mechanics. He states that the wave function ##\psi## approaches 0 as x approaches infinity to make normalization work. I can accept that. But then I...

I had two questions in the field of physics: We know that in quantum mechanics there is an electron in a certain distance from the distance to the nucleus as a cloud or a cover. But is motion for the cloud defined by the electron moving around the nucleus? And the main question is, can the...

Here is what I tried. Suppose ##f(\phi)## and ##\lambda## is the eigenfunction and eigenvalue of the given operator. That is, $$\sin\frac{d f}{d\phi} = \lambda f$$ Differentiating once, $$f'' \cos f' = \lambda f' = f'' \sqrt{1-\sin^2f'}$$ $$f''\sqrt{1-\lambda^2 f^2} = \lambda f'$$ I have no...

fidelity for pure state with respect to t=0 is 1. My teacher told me this. But I am not getting this. This is my detailed question the initial state(t=0)##|\psi\rangle=|\alpha\rangle|0\rangle## the final state (t) ##|\chi\rangle= |i\alpha\sin(t)\rangle|cos(t)\alpha\rangle## Fidelity between the...

Hello! If I place a particle with more energy levels (of the order of kT) in a well defined state, in a thermal bath at temperature T, how will the blackbody radiation affect the internal state of the particle i.e. will the distribution be classical or QM? Basically, if I prepare that particle...

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit coupling in Hydrogen atom arises from the interaction between the electron’s spin magnetic moment...

Robert Lawrence Kuhn: It seems that special relativity suggests time is like gravity and electromagnetism, not built into the absolute fabric of reality like logic and causation. David J Gross: Yes, time is dynamical. The phenomena are dynamical and are labeled by what we call time. Including...

Observables on the "3 polarizers experiment" Hi guys, I was analyzing the 3 polarizers experiment. This one: (first 2 minutes -> ) Doing the math (https://faculty.csbsju.edu/frioux/polarize/POLAR-sup.pdf) I realized that the process is similar to the Stern-Gerlach' experiment. Using spins...

Is it likely that this year's Nobel prize could be awarded to the field of quantum cryptography with Charles H Bennet, Gilles Brassard and Artur Ekert as possible nobel laureate candidates?

In general, if R is the recovery channel of an error channel ε, with state ρ, then and according to these lecture slides, we get the final result highlighted in red for a bit flip error channel. I am simply asking how one reaches this final result. Thank you (a full-ish derivation can be found...

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I have written and rewritten a lot of times but I need some fresh eyes on my sop. It would be great if someone can help me out. I have less than a week to readjust it and send. My motivation to apply for the Masters Degree in quantum engineering at University of Wurzburg is to...

So initially I thought quantum mechanics was deterministic in the equations but was probabilistic in measurement. I’m aware of bell’s inequality which rules out hidden variables unless you assume super determinism. But recently I’ve come across something called decoherence and some people have...

While reading in the book of Introduction to Quantum Mechanics by David Griffith in the section of Fine structure of Hydrogen: spin- orbit coupling, he said that the average value of S operator is considered to be the projection of S onto J. I could not understand why he assumed that. please...

Hello everyone. I am studying physics as a self-study and would like advice on the next topics to study. So far I have been studying: -calculus, linear algebra and basic physics -classical mechanics (from Goldstein's textbook) -classical electrodynamics and special relativity (from Griffiths...

intermolecular distance means distance between particles. So, I imagine a sphere. $$\frac{4}{3} \pi d^3 = \frac{V}{N}$$ However, Griffitfhs pictures a box instead, where $$d^3 = \frac{V}{N}$$ And the difference between both models is a factor of ##(4\pi/3)^{2/5} \approx 1.8##, which is...

Let's play this game, let's assume the infinite Hilbert Space, the operators and all the modern machinery introduced by Von Neuman were not allowed. How would be the formalism? Thanks

A certain field has a singularity at the origin, and the divergence of its curl is zero at any point outside the origin, but surface integral of the curl is not zero in the area of any closed surface containing the origin. So how should the Stokes theorem related to this field be expressed at...

If we prepare a macroscopic system (something like Shrodinger's cat) in a known quantum-mechanical state and we let it evolve for a very long time completely isolated, for what I understand the position of all it's particles will become more and more spread in space. But if the evolution of the...

{a} P = identity Matrix w/ -1 on diagonals {b} eigenvalues = +/- 1

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...

I noticed the research on NHQM in the following news release. New physics rules tested on quantum computer Published: 19.2.2021 Information for relevant paper is provided as follows. Quantum simulation of parity–time symmetry breaking with a superconducting quantum processor Shruti Dogra...

I am getting that we have to operate the given Hamiltonian on the given state |α>. But what is confusing me is that since this H contains position and momentum operators which just involve variable x and partial derivative, how do I operate this H on the given α, since it seems like α is...

I began this solution by assuming a = x+iy since a is a complex number. So I wrote expressions of <a| and |a> in which |n><n| = I. I got the following integral: Σ 1/πn! ∫∫ dx dy exp[-(x^2 + y^2)] (x^2 + y^2)^n I I tried solving it using Integration by Parts but got stuck in the (x^2 + y^2)^n...