Heisenberg Definition and 311 Threads

Is the Heisenberg Uncertainty Principle (HUP) applicable to macroscopic objects? A football, for instance, is composed of an enormous number of particles. Can the applicability of the HUP to a macroscopic object like a football be demonstrated through statistical methods, starting from the...

Heisenberg uncertainty principle relates to the limitations on the precision with which certain pairs of physical properties (like position and momentum) of a particle can be simultaneously known. The uncertainty relations for position and momentum as operators arise from the non-commutative...

Hi. I was just wondering. Why does Heisenberg's principle of indeterminacy say that we can't know the position and velocity (momentum) of a particle with any precision, when a particle isn't point-like anyway? It's like the position of a car, it's arbitrary and all we can say about its...

Consider the Heisenberg picture Hamiltonian $$H(t) = \int_{\textbf{r}}\psi^{\dagger}(\textbf{r},t)\frac{(-i\hbar\nabla+e\textbf{A})^{2}}{2m}\psi(\textbf{r},t)$$ where ##\psi(\textbf{r},t)## is a fermion field operator. To find the equations of motion that ##\psi,\psi^{\dagger}## obey. I would...

In the youtube lecture “electron interaction and the Hubbard model” at the time 2:23:00, we have the following self-consistent equation with energy appearing at both sides: $$(\hat P \hat H_0 \hat P+\hat P \hat H_1 \hat Q (E-\hat Q \hat H_0 \hat Q)^{-1} \hat Q \hat H_1 \hat P) |\phi...

here is my attempt to implement using python import numpy as np import matplotlib.pyplot as plt def initialize_spins(L): """Initialize a random spin configuration with unit magnitudes.""" spins = np.random.normal(size=(L, L, L, 3)) magnitudes = np.linalg.norm(spins, axis=-1...

How is the Schrondinger equation related to the Heisenberg equation?

Hi all, This should be a simple question but it has been bothering me for a bit: Consider 2 Hamiltonian terms ##H_{1},H_{2}## that satisfy ##[H_{1},H_{2}] = 0##. Suppose we are working in the Heisenberg picture and we time evolve some operator ##A## according to ##A(t) =...

When I'm teaching Advanced QM, I like to include how to describe some processes in the Heisenberg picture (e.g. double slit) so that a student's thinking isn't overly attached to the "dynamics of the quantum state", but they can also understand effects involving operator evolution. This is a...

Reading the introduction to path integrals given in the latest edition of Zee's "Quantum field theory in a nutshell", I have found a remark which I don't really understand. The author is evaluating the free particle propagator ##K(q_f, t; q_i, 0)## $$\langle q_f\lvert e^{-iHt}\lvert q_i...

We know from basic quantum mechanics that the Heisenberg uncertainty states that position and momentum can not be measured simultaneously with arbitrary precision. My question is, is this relation is due to the nature of the quantum system itself, or "merely" unbreachable limitation to our...

Heisenberg is regarded as a major figure of the Copenhagen interpretation. In a certain degree, he is influenced by Logical positivism. Despite of that, has he any ontological commitments regarding the Quantum theory? Or, he considers the Quantum theory merely as calculation procedure for...

So, I have a hamiltonian for screening effect, written like: $$ H=\sum_{k}^{}\epsilon_{k}c_{k}^{\dagger}c_{k}+ \frac{1}{\Omega}\sum_{k,q}^{}V(q,t)c_{k+q}^{\dagger}c_{k} $$ And I have to find an equation for the time evolution of the expected value of the operator ##c_{k-Q}^{\dagger}c_{k}##. I...

We have commutation relation ##[J_j,J_k]=i \epsilon_{jkl}J_l## satisfied for ##2x2##, ##3x3##, ##4x4## matrices. Are in all dimensions these matrices generate ##SO(3)## group? I am confused because I think that maybe for ##4x4## matrices they will generate ##SO(4)## group. For instance for...

Hello, 2 questions please about the Uncertainty Principle and the following scenario: I shoot at each other, 2 electrons each with equal but opposite velocity such that they repel each other? (To me, this indicates that you know the momentum of each electron and you know each position...

In post #30 of a now closed thread, vanhees71 wrote: The quote in question is from his 1930 book "The Physical Principles of the Quantum Theory" on p.20 of the English translation of the German original. There Heisenberg writes:

Hi Pf in her experiment Birgit Dopfer uses an https://www.researchgate.net/figure/color-online-The-Dopfer-experiment-of-the-Zeilinger-Group-Innsbruck-If-detector-D2-is_fig7_265787833 the distance between the source and the lens is 2f and the detector may be at the distance f or 2f behind the...

Suppose that a particle evolves from point A to point B. The state of the particle can be written as $$\rho=\sum \left | m\right >\rho_{mn}\left< n\right | .$$ Because the basis is evolving as the particle travels, I am considering applying the Heisenberg picture to the density operator. Let...

Heisenberg equation of motion for operators are given by i\hbar\frac{d\hat{A}}{dt}=i\hbar\frac{\partial \hat{A}}{\partial t}+[\hat{A},\hat{H}]. Almost always ##\frac{\partial \hat{A}}{\partial t}=0##. When that is not the case?

How do you prove Heisenberg uncertainty relations for mixed states (density matrix), only from knowing the relation is true for pure states?

Hello, I am a Brazilian Physics student and would like to ask a question. Why are not all physical quantities related to each other by the degree of precision in the Heisenberg Uncertainty Principle? For example, why is it possible to determine the energy and position of a particle without its...

In the thought experiment proposed by Heisenberg, a single photon is scattered by the electron that we want to observe, and entering the microscope lens (the photon), it will create a diffraction pattern that gives the uncertainty on the position according to the law of optics. I wanted to ask...

So there's this professor who insists that the Heisenberg picture is all the rage and much superior in most ways to the Schrodinger picture. He compares it to how you don't use the Hamilton-Jacobi formulation of classical mechanics as much as the Hamiltonian one. Alright, I can buy it. I...

Hi people. Having as uncertainty principle that ΔE Δt≥ h/4Pi, why Δt≤ h/4PiΔE to allow the existence of a virtual particle? How ≥ becomes ≤ ? I think... real particles must obey ≥ so any particle that do not obey that is a virtual particle and thus why virtual particle needs to obey Δt≤...

Hi! I am checking Zettili's explanation on the uncertainty principle and I have this confusion on what the "uncertainty" really means which arises from the following statements: When introducing the uncertainty principle, for the case of position and momentum it states that: if the x-component...

Consider the classical Heisenberg model without an external field which is defined by the Hamiltonian: \mathcal{H} = -\sum_{ij} J_{ij} \vec{s_i}\vec{s_j} where J_{ij} > 0 describes the coupling between the spins \vec{s}_i \in \mathbb{R}^3 on some lattice. (Is there a way to use tex...

Hi, there. I am reading An Introduction to Quantum Field Theory by Peskin and Schroeder. I am confused about some equations in section 2.4 The Klein-Gordon Field in Space-Time. It computes the Heisenberg equations of ##\phi \left ( x \right )## and ##\pi \left ( x \right)## as (in page 25) ##...

Good Morning When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative). I do understand that this is allowed: we are trying to find...

I have some problems when calculating the operators in Heisenberg picture. First, ##\frac {dx} {dt} = \frac {1} {i \hbar} \left [ x, H \right ] = \frac {p} {m}##. Similarly, ##\frac {dp} {dt} = \frac {1} {i \hbar} \left [ p, H \right ] = - m \omega ^ 2 x##. These are coupled equations. I...

While reading a book "Physics and Philosophy: The Revolution in Modern Science." by Werner Heisenberg, 1958, I was much surprised by the following passage near the end of Chapter 3: "The measuring device deserves this name only if it is in close contact with the rest of the world, if there is...

When a quantum measurement occurs under the Schrodinger picture, the wave function collapses to one of the eigenvectors of the operator-observable and the value measured is the corresponding eigenvalue of that eigenvector. What happens during a quantum measurement under the Heisenberg picture...

why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

In quantum mechanics the name is Uncertainty principle. But outside of QM, what is the name for those inequalities?

A 2019 paper by Gorecki et al. derives an uncertainty principle limit that is larger than the conventional Heisenberg limit by a factor of ##\pi##: https://arxiv.org/abs/1907.05428 I'm wondering if any QM experts have seen this and what your thoughts are.

I have a problem about Heisenberg model.When applying mean field approximation,why does the average of spin flip terms be zero(<S+>=<S-> = 0 )? Thanks

This is in reference to a question, never fully resolved, posed here: https://www.physicsforums.com/threads/interpretation-of-the-heisenberg-picture-in-qm.816449/ The von Neumann postulates for Quantum Theory - Evolution (Schrödinger's equation) and Projection (Born's rule) are always framed...

Homework Statement From Griffiths GM 3rd p.266 Consider a free particle of mass ##m##. Show that the position and momentum operators in the Heisenberg picture are given by$$ {\hat x}_H \left( t \right) ={\hat x}_H \left( 0 \right) + \frac { {\hat p}_H \left( 0 \right) t} m $$ $$ {\hat p}_H...

Symmetry transformations are changes in our point of view that preserve the possible outcomes of experiment: $$\Psi \rightarrow U(\Lambda) \Psi$$ In the Heisenberg picture, observables in a fixed reference frame evolve according to: $$P(t) = U^\dagger (t)PU(t)$$ while in the Schrodinger...

To summarize, my current understanding of how Heisenberg's uncertainty principal works suggests that there would be a contradiction (somewhere down the line) with any way that it applies to (or doesn't apply to) photons, due to the fact that they must always travel the speed of light. I...

heisenberg uncertainty principle ## Δx Δp ≥ ħ## where ##Δx = \sqrt{<\hat{x}^2>-<\hat{x}>^2}## ##Δp = \sqrt{<\hat{p}^2>-<\hat{p}>^2}## I don't know. Why ##Δx## equal to ## \sqrt{<\hat{x}^2>-<\hat{x}>^2} ## and ## Δp ## equal to ## \sqrt{<\hat{p}^2>-<\hat{p}>^2} ## What can I find out about...

I have seen that the more a particle has a high energy, i.e ##E##, the more its lifetime is short, respecting so the uncertainty principle. But by the definition of this uncertainty principle : ##E\,\Delta t \geq \dfrac{\hbar}{2}##, I can write : ##\Delta t \geq \dfrac{\hbar}{2E}##, then...

I'm studying plasmons from "Haken-Quantum Field Theory of Solids", and i need some help in the calculation of the equation of motion of eletrons' density \begin{equation} \hat{\rho}_{\overrightarrow{q}} = \frac{1}{\sqrt{V}} \sum_{\overrightarrow{k}}...

Hi physics forms! I'm practicing to for an Quantum mechanics exam, and i have a problem. 1. Homework Statement I have two problems, but it's all related to the same main task. I have a state for the Hydrogen: ## \Psi = \frac{1}{\sqrt{2}}(\psi_{100} + i \psi_{211})## where ## \psi_{nlm}##...

to begin with I am a biophysicist so my question is very naive. It is my understanding that the Uncertainty Principle deals with a single event (particle). It is also my understanding that quantum physics contains a lot of statistics (probability). The question is: in the area of...

Has anyone conjectured that the redshift associated with Hubble's constant can be explained by Heisenberg's uncertainty principle? Another words, the further in space away from us a photon is emitted from a galaxy, the longer in time it takes for the photon to reach us. Since the photon has a...

Hi! I am a bit confused about something Heisenberg said about the wave-particle dualism. In his book about physics and philosophy he wrote: "The dualism between the two complementary pictures - waves and particles - is also clearly brought out in the flexibility of the mathematical scheme. The...

Spun off from https://www.physicsforums.com/threads/is-quantum-physics-retro-deterministic.945431/#post-5984157. @Gerinski said: if we measure a particle's position at time X (not caring about its momentum) and we measure it again at a later time Y and we find it at some other position (again...

I was musing about why the HUP is an inequality. If you analyse a wave packet the spatial frequency spectral width is inversely proportional to the spatial width. So there should be an equality such as Heisenberg's equation 3 in this paper. Has anyone got a simple explanation of where the...

Is it somehow possible to know both noncommutating properities of eg. a partcle, with using two indicators? Eg. two teams, with one is studing the momentum, and other one the position - then it's somehow impossible to exchange informations?

Hey everybody, I am trying to expand a system of seven qubits from one dimensional Hamiltonian to the two dimensional representation. I have the one dimensional representation and I don't know what to add to transform it from 1D to 2D representation. I would really appreciate your help and...