Heisenberg Definition and 309 Threads

The standard Heisenberg picture equation of motion is $$i\hbar\frac d{dt}A_H=[A_H,H],$$ assuming no explicit ##t##-dependence on the Heisenberg-picture operator ##A_H##. I've been trying to go directly from this equation to the corresponding interaction-picture equation, $$i\hbar\frac...

One thing that's been troubling me lately is the idea that a quantum experiment can start with the same initial conditions, but the outcome is probabilistic, not deterministic, and how this fits in with the conservation of momentum. I was thinking about the classic double-slit experiment, in...

Hello when I try to go form the Schrödinger picture to the Heisenberg picture I get this equality : \begin{align} {d \over dt} A(t) = {i \over \hbar} H e^{iHt / \hbar} A e^{-iHt / \hbar} + e^{iHt / \hbar} \left(\frac{d A}{d t}\right) e^{-iHt / \hbar} + {i \over \hbar} e^{iHt / \hbar} A \cdot...

So I understand that Heisenberg Uncertainty states that we cannot know the position and velocity of an electron at the same time. Although I haven't go through its proof and assumptions, I have read on couple place that that's because if we are able to observe it, that means it have to reflect...

Why does Heisenberg picture formalism requires to rewrite operators in explicit covariance?

I would appreciate if someone could help figure out this thought experiment: Lets say I have two detectors named A and B. They both want to detect system C. For my naming convention I will say that C.B is the perturbed state of C after interacting with B Ok so both A and B decide to measure...

I've applied physics in nuclear weapons work, finance, biochemistry, molecular dynamics, space physics, and other areas. High school students, and even young Air Force officers with technical degrees often have little idea of the value of physics. And physics loses. Linked here to a Prezi...

I am looking at the derivation of the Heisenberg Uncertainty Principle presented here: http://socrates.berkeley.edu/~jemoore/p137a/uncertaintynotes.pdf and am confused about line (21)... I do not understand why AB and BA are complex conjugates of each other... (I'm still in high school so I...

Two questions about the path integral: a) Intuitively, how does one (as Landau does) start quantum mechanics from Heisenberg's uncertainty principle, which states there is no concept of the path of a particle, derive Schrodinger equation i \hbar \tfrac{\partial \psi}{\partial t} = H \psi the...

I would like to know more about how Heisenberg developed his matrix mechanics.He wanted to represent the quantum state in terms of observable quantities such as spectral frequencies and intensities,rather than via the more abstract wave function of Schrodinger.But how did he assemble the arrays...

Homework Statement A bullet is shot from a rifle. 1) if the position of the centre of mass of the bullet perpendicular to its motion is known to have an accuracy of 0.01 cm, what is the corresponding uncertainty in its momentum? 2) If the accuracy of the bullet were determined only by the...

Homework Statement These questions are out of Modern Physics by Tipler. I feel like I'm close to the answer but missing something small. #1: A ladybug 5mm in diameter with a mass of 1 mg being viewed through a low power magnifier with a calibrated reticule is observed to be stationary with an...

I'm studying the SU(3) invariant XXX chain as part of my Bachelor's thesis. The monodromy matrix of this system can be written as a 3x3 matrix. We perform a 2x2 decomposition of it and write is as ##T(\mu)=\left( \begin{array}{cc} A(\mu) & B(\mu) \\ C(\mu) & D (\mu) \end{array} \right)## For a...

I came across two different forms of Heisenberg uncertainty: \Delta x . \Delta p \geq \frac{h}{2 \pi} and \Delta x . \Delta p \geq \frac{h}{4 \pi} and I read here in PF both forms are correct. I want to know how we apply both forms in solving problem. Here is the example: 1. An electron...

Does the Heisenberg Uncertainity Principle mean: 1) If a particle is confined within a length x then it must jiggle around with a momentum given by p ~ h/2x PI OR 2) If we measure the position of a particle to an accuracy of x then its momentum will be uncertain by ~ h/2x PI

Homework Statement An electron is trapped in a one-dimensional well of width 0.132 nm. The electron is in the n = 10 state. a) What is the energy of the electron? b) What is the uncertainty in the momentum? c) What is the uncertainty in the position? Homework Equations En = h2n2/8mL2...

I was wondering how to derive hamilton's equation (in the form of poisson brackets) from Heisenberg's equation of motion

A paper I'm reading says "Our starting point is the SU(N) generalization of the quantum Heisenberg model: H=-J\sum_{\langle i,j \rangle}H_{ij}=\frac{J}{N}\sum_{\langle i,j \rangle}\sum_{\alpha , \beta =1}^N J_{\beta}^{\alpha}(i)J_{\alpha}^{\beta}(j) The J_{\beta}^{\alpha} are the generators of...

Coming from a Chemistry background, the Uncertainty Principle always seemed to be described as an inability of precision due to strictly physical and real reasons (i.e. you have to interact with an object to measure something about it, and this certainly will alter the object). It seems as if...

I've usually heard the many-worlds interpretation described in the Schroedinger picture, in which the wave function evolves unitarily. Does a Heisenberg picture exist for many-worlds, or is the Schroedinger picture more fundamental in that interpretation?

I would expect that the Heisenberg equation of motion for the Dirac field would yield the Dirac equation. Indeed, these lecture notes claim it as a fact in eq 7.7 but without proof. My trouble is that I know the anti-commutation rules for the Dirac field but I don't know how to calculate the...

I have some questions regarding the Heisenberg picture of QM. 1. How does one calculate probabilities for measuring eigenvalues? Are the eigenvectors simply time dependant? 2.Does this mean for initial value problems, the initial data of the system is contained in the operators? (Or...

Hello, Can anyone recommend me a book that develops QFT in Heisenberg picture? I have found Källen - Quantum Electrodynamics. Thanks in advance for the answers.

Hi fellas, one friends that is Mathematician asked me to recommend some textbook that emphasizes Heisenberg picture and where this picture is rigorously explained. If anyone knows some good book for this I would be grateful :) Regards, Ivan

Homework Statement Explain, using the Heisenberg Uncertainty Principle, how classical physics is reached a a limit of quantum physics when (h-bar) tends to 0. Homework Equations ΔxΔp(x) ≥ (h-bar)/2 The Attempt at a Solution The only reasonable answer I can formulate is the fact that when...

In deriving the Heisenberg uncertainty relation for 2 general Hermitian operators A and B , the uncertainty operators ΔA and ΔB are introduced defined by ΔA=A - (expectation value of A) and similarly for B. My question is this - how can you subtract(or add) an expectation value , which is just...

Hi, I'd like to argue Heisenberg doesn't apply to a collapsed wave... I always interpretted the Heisenberg Uncertainty Principle (HUP) as follows: 1. HUP is *not* about measurement problems, it is fundamental 2. When (f.i.) an electron is a wave: HUP applies. The electron really *has*...

I was given the (general) following form for the Hamilton and Heisenberg Equations of motion \dot{A} = (A, H)_{}, which can represent the Poisson bracket (classical version) or \dot{A} = -i/h[A,H] (Quantum Mechanical commutator). I was given the general solutin for A(t) = e^{tL}A...

For two electron system ##\vec{S}_1##, ##\vec{S}_2## \mathcal{H}=J\vec{S}_1\cdot \vec{S}_2=J(\frac{1}{2}(S_{tot})^2-\frac{3}{4}) (1) How you get relation (1)?

I don't know much about physics but just had this idea: As I understand it the HUP prevents good accuracy of a small object's momentum and position at the same time. Assume trying to measure the momentum and position of a single atom. In theory, can't we get a very good idea of both of...

I know I have seen this before a few time done a few different ways/starting points and I am always blown away when I see it worked out. Don't know why but I love seeing this derivation. Does anyone want to post the derivation for all to see, it being done a few different ways would be great.

Homework Statement A particle of mass m is in a harmonic oscillator potential with spring constant k. An observable quantity is given in the Schrodinger picture by the operator: Z = a^{\dagger}a a^{\dagger} a a) Determine the equation of motion of the operator in the Heisenberg...

Hey guys, Imma type this up in word so its nice and clear! http://imageshack.com/a/img32/2013/3q8s.jpg

I am reading the book "Lecture notes on Electron Correlation and Magnetism" by Patrik Fazekas. It says, "The ground state (of Heisenberg FM model) is not unique. We have just found that the system has the maximum value of the total spin Stot = LS. Sztot = LS state which is maximally...

It is obvious to me how \hat {x} = x; \hspace{5 mm} \hat {p}_x = -i \hbar \frac {\partial} {\partial x} implies [ \hat {x} , \hat {p}_x ] = i \hbar and I can accept that these two formulations are mathematically equivalent, but I do not know how in general (or even in this specific...

I read somewhere that Heisenberg described his uncertainty principle by saying that you can't measure position more accurately than the wavelength of light (which makes sense), so Δx > λ. This is what I don't get. He then says that p=h/λ, so Δp > h/λ2 Δλ. He the multiplies and sets Δλ ≈ λ to...

in quantum mechanics, these same pairs of variables are related by the Heisenberg uncertainty principle. The energy of a particle at a certain event is the negative of the derivative of the action along a trajectory of that particle ending at that event with respect to the time of the event...

Homework Statement For the ground state of a particle in a rigid box, we have seen that the momentum has a definite magni- tude (h/2π)k but is equally likely to be in either direction. This means that the uncertainty in p is Δp≈ (h/2π)k. The uncertainty in position is Δx≈ a/2. Verify that...

Hey guys, I saw a joke about this in the jokes thread. So I went to see what it is exactly. But the thing is I didn't understand it fully. Could anyone please simplify and comprehend to me? Also I saw that it's only for particles. What is the importance of this theory. I hope non complicated...

In quantum Heisenberg model \hat{H}=-J\sum_{\vec{n},\vec{m}}\hat{\vec{S}}_{\vec{n}}\cdot \hat{\vec{S}}_{\vec{m}} ##J## can be obtained from dispersion experiment. For large spin ##S## even classical Heisenberg model is good for description of Curie temperature for example. Is that with the same...

A = \langle q_f(t) \mid q_i(t) \rangle = \langle q_{f,H} \mid e^{iH(t_0-t)} e^{-iH(t-t_0)} \mid q_{i,H} \rangle = \langle q_{f,H} \mid q_{i,H} \rangle This means that A is time-independent, and depends only on the reference point ##t_0##. How is it possibly? From Schoedinger picture it...

Homework Statement In special conditions, it is possible to measure the energy of a gamma ray photon to 1 part in 10^15. For a photon energy of 50 keV, estimate the maximum lifetime that could be determined be a direct measurement of the spread of photon energy. Homework Equations...

I'm not certain as to the true meaning of the Heisenberg Uncertainty Principle, and wonder if anyone can provide insight. I understand that there is a reciprocal relation between the certainties as to the position and momentum of a particle such as an electron; the more precisely position is...

I did a Fourier transform of a gaussian function ##\scriptsize \mathcal{G}(k) = A \exp\left[-\frac{(k-k_0)^2}{2 {\sigma_k}^2}\right]## and derived a result ##\sigma_k \sigma_x = 1## which is the same they get on http://www4.ncsu.edu/~franzen/public_html/CH795Z/math/ft/gaussian.html. Here is a...

Hi does anyone know how bogulobov transformations are related to the Heisenberg uncertainty principle?

Homework Statement Calculate the spin wave dispersion relation Ek for the ferromagnetic Heisenberg model with jtot = 1/2 Assume a 1d square lattice and interactions of strength J between nearest neighbours and zero elsewhere Homework Equations H|k> = [E0 +2jtot\sum J(r)(1-Exp(ik.r) ]...

Say you have a particle in a one-dimensional box of length L. The particle can only have momentum values of the form p_{n} = \frac{nh}{2L} according to the De Broglie standing wave condition. Now say I don't measure the position of the particle, but I know for certain that it is in the box...

In several textbooks of QM I have read that Lorentz invariance is manifest in Heisnberg picture. How can we deduce that?

Hi, I just started self studying solid state and I'm having trouble figuring out what the hamiltonian for a square lattice would be when considering the Heisenberg interaction. I reformulated the dot product into 1/2( Si+Si+δ+ +Si+δ+S-- ) + SizSi+δz and use Siz = S-ai+ai Si+ =...

Hello! I have a doubt about Heisenberg uncertainty principle. Suppose that a particle moves along x-axis with a given uncertainty in velocity. Can I say something about its motion along y-axis? Thanks