The hybrid QM/MM (quantum mechanics/molecular mechanics) approach is a molecular simulation method that combines the strengths of ab initio QM calculations (accuracy) and MM (speed) approaches, thus allowing for the study of chemical processes in solution and in proteins. The QM/MM approach was introduced in the 1976 paper of Warshel and Levitt. They, along with Martin Karplus, won the 2013 Nobel Prize in Chemistry for "the development of multiscale models for complex chemical systems".
So I think I use the right approach and I get uncertainty like this:
And it's interval irrelevant(ofc),
So what kind of wave function gives us \h_bar / 2 ? I guess a normal curve? if so, why is normal curve could be? if not then what's kind of wave function can reach the lower bound
Forgive my poor lingo. As my bio states, I only have a complete degree in HS.
Is it possible to quantum tunnel across possible worlds?
If so, is there a hyper-dimensional plane where this would be made possible?
And if so, how would you conceptualize or describe it?
Information breakage...
So, I was in class listening to my lecturer when I notice something intriguing. I was looking at the reflection of a lamp on the screen of my calculator. I paid close attention to the colour of the light reflected of my calculator and realised that when I rotate my calculator by about 90 deg...
Sabine Hossenfelder has a recent thread on her blog about experiments in physics, talking about how much money is spent on dark matter and what not. I actually wanted to open a thread even before that. My observation is that the field of experimental physics in foundation seem to be so thin and...
I get new notification from new scientist usually about some virus or some weird anthropology theory. Once in a while a physics subject and this time I got this "https://www.newscientist.com/article/mg24132220-100-schrodingers-kittens-new-thought-experiment-breaks-quantum-theory/"
Can somebody...
Homework Statement
Consider an electron in a hydrogen atom in the presence of a constant magnetic field ##B##, which we take to be parallel to the ##z##-axis. Without the magnetic field and ignoring the spin-orbit coupling, the eigenfunctions are labelled by ##\vert n, l, m, m_s \rangle##...
Homework Statement
This isn't exactly a problem but rather a problem in understanding the derivation of the phenomenon, or more precisely, one step in the derivation.
In the following we will consider the EPR pair of two spin ##1/2## particles, where the state can be written as
$$ \vert...
Homework Statement
Consider a 2-particle system where the two particles have angular momentum operators ##\vec{L}_1## and ##\vec{L}_2## respectively. The Hamiltonian is given by
$$H = \mu\vec{B}\cdot (\vec{L}_1+\vec{L}_2)+\gamma \vec{L}_1\cdot \vec{L}_2.$$
Determine explicitly the eigenvalues...
There are two recent threads about the subject, however I want to ask a different question.
What does the wavefunction is "real" imply or what such "clarification" actually mean to the deeper understanding of QM. The theory is purported to be revolutionary and important breakthrough, yet it...
Homework Statement
Let ##U_t = e^{-iHt/\hbar}## be the evolution operator associated with the Hamiltonian ##H##, and let ##P=\vert\phi\rangle\langle \phi\vert## be the projector on some normalized state vector ##\vert \phi\rangle##.
Show that
$$\underbrace{PU_{t/n}P\dots PU_{t/n}}_{n\text{...
Homework Statement
Prove that the Clebsch-Grodan coefficients (in the notation ##\langle j_1j_2m_1m_2|j_1j_2jm\rangle##) for the decomposition of the tensor product of spin ##l## and spin ##1/2## to spin ##l+1/2## are
$$\left\langle l,\frac{1}{2},m\mp \frac{1}{2}, \pm \frac{1}{2} \Bigg\vert l...
In Classical Mechanics, according to SR, the concept of simultaneity is dead, a meaningless concept. But in QM, entanglement implies that some limited form of simultaneity exists. If we have two particles correlated due to entanglement, a measurement of one particle immediately gives us the...
If we use a probabilistic model of QM, is there still room for determinism? If we don't have knowledge of the exact outcomes, can there still be underlying determinism in such a model?
I am aware there are probabilistic and deterministic models available for QM. Does that mean QM could be...
I was reading this paper
https://arxiv.org/pdf/0805.4725.pdf
It seems that the potential between the particles can be assumed of different forms, shouldn't the potential be a solution of the problem.
Thanks
I read this wiki and some of the references
https://en.wikipedia.org/wiki/Bound_state
But I can't really understand. For example the electron in hydrogen has specific energies and not general relations that the articles seem to claim.
Thanks
I mean the equation shows the particle could have any momentum, how did that came about. If it is truly free it should have only an energy of mc^2, shouldn't it.
Homework Statement
A particle is moving in a 1-dimensional harmonic osciallator with the hamiltion:
## H = \hbar \omega (a_+ a_- + \frac{1}{2})##
at time ## t=0## the normalized wave function is given by
## \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x) + i\psi_1(x)) ##
Task: Calculate for ## t \geq...
Homework Statement
A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator:
H = \hbar \omega (a_+ a_- + \frac{1}{2})
at t = 0 we have
\Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x))
Find the expectation value and variance of harmonic oscillator...
Hello
Can somebody explain for me what is the meaning of inversion symmetry in solids?
and why does it breaks at the surface?
and also why this inversion symmetry breaking leads to SOC(spin orbit coupling)?
If somebody also know a document that explain this in full details(from A to Z) please...
Hi, are there any models known in QM where the wavefunctions do not have to be infinitely differentiable, and thus can exist in other spaces than the Hilbert space? I assume Banach spaces allow elements that are not infinitely differentiable as subsets. Can therefore certain phenomena in QM be...
Homework Statement
Hi all, I'm working on the following problem and would like some help. Many thanks in advance!
The Figure below presents the Mach-Zehnder interferometer with an additional phase shift element in the upper path.
$$\left( \begin{array}{cc}
e^{i\phi} & 0 \\
0 & 1
\end{array}...
Suppose we have a particle, lets say an electron, in a box of size D. And we add another one next to it at some distance L center to center. How do we solve for the wavefunctions of the electron. Can it be solved in normal QM or do we need QFT. Thanks.
Hi, I found this article very interesting, given the loads of question I have posted in this regard in the last months. I cannot recall where I got the link from, and if it came from Bill Hobba in some discussion, thanks Bill! If not, thanks anyway for your answers and contributions.
Here is...
In the original EPR paper momentum was giving as an example of entanglement, but I don't see that discussed by any thread or papers for that matter, why is that. What is the technicalities of this entanglement for two electrons for example, is it also instantaneous and why is it not used to...
Homework Statement
I am supposed to find probability of staying in x < 0 for a superposition of two Gaussians. The wavefunction is something along the lines of:
Homework Equations
The Attempt at a Solution
Usually, the step involved in finding probabilities for 1 particle is just to...
Homework Statement
I've been asked as a part of some school project to find the fourier transform, and time evolution of the following initial wavefunctions:
1. ##\Psi(x,0) = Ae^{\frac{-x^2}{2\sigma ^2}}##
2. ##\Psi(x,0) = Be^{\frac{-x^2}{2\sigma ^2}}e^{\frac{ipx}{\hbar}}##
What physical...
Is the measurement problem in QM addressed and solved by now?
If not, can we speak of QM as a description of reality?
Given the statistical nature of QM, can we say it predicts reality?
What is it that QM addresses?
I'm having a hard time understanding 'degrees of freedom'. Could someone please provide an example in terms of Quantum Mechanics about what a 'degree of freedom' could be represented as? Is it simply a number of observations of a physical system to determine the arrangement of particles within...
Hi all, I'd like some assistance regarding some issues I have understanding such states. (Referencing Griffiths' QM)
1) Meaning of Bound and Scattering States.
The bound states I have studied thus far are limited to the infinite square well and the quantum harmonic oscillator. In the case of a...
Homework Statement
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1) I don't quite understand what 2.94 means on its own. It was derived from 2.93, yet it doesn't show a superposition of any sort. The author then takes 2.94, and attempts to normalise it by stating
##\int \Psi_k^* \Psi_k dx = \mid A^2 \mid\int dx = \infty ##
What...
1. Problem
Recall that we defined linear equations as those whose solutions can be superposed to find more solutions. Which of the following differential/integral equations are linear equations for the function u(x,t)? Below, a and b are constants, c is the speed of light, and f(x,t) is an...
In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation?
Could you tell me whether following is true...
I joined this site because I had questions and wanted to discuss topics on the subject of black holes. Lenny Susskind's lecture of this topic raised quite a few question a and ideas in my mind. I did write my concerns in the comments for the video, but I'll just paste that here as well. Here's...
This might become a series of questions, but let me begin with the most essential one.
According to QM/QFT, would it be true that there is a non-zero chance for an object on earth to instantaneously tunnel to the moon for example?
Like let's say a paper with a note on it. Could this paper...
using the references below, the effective charge and the potentials are derived for either r >> 1/m or r << 1/m, so what happens between these two distances. Thanks
https://en.wikipedia.org/wiki/Vacuum_polarization
https://en.wikipedia.org/wiki/Uehling_potential...
Homework Statement
So we have a two state system, with unperturbed eigenstates ## |\phi_{1}\rangle##, ## |\phi_{2}\rangle ##, and Hamiltonian ## \mathbf{\hat{H_{0}}}## - i.e ##\mathbf{\hat{H_{0}}}|\phi_{1}\rangle = E_{1}|\phi_{1}\rangle##
We shine some z-polarized light on the system. This...
I am a laymen of sorts in both physics and philosophy. I embarked on a trip to acquaint myself (gently at first) with contemporary physics. My question is foundational and therefore probably philosophical. If it is off-topic, please kindly point me to any place where such discussions may be...
I'm currently a junior in high school, and I'm really interested in physics, especially particle physics and quantum mechanics. At my school, everybody needs to do a big senior project to graduate, involving multiple papers and about 30 hours of work, usually to build something or organize a...
Could physics ever be able to confirm that a certain interpretation of quantum mechanics is correct or is the matter entirely philosophical and thus doomed to the depths of subjectivity?
I'm from a country in Africa where I didn't have the privilege of learning the Standard Model, so I'll try and rephrase my question here:
https://www.physicsforums.com/threads/why-is-the-electromagnetic-field-not-a-charge-field.857927/#post-5384284
In a way where my ignorance doesn't outrage...