Heisenberg Definition and 309 Threads

Homework Statement Given for one-dimensional Galilean symmetry the generators ##K, P,## and ##H##, with the following commutation relations: $$[K, H] = iP$$ $$[H,P] = 0$$ $$[P,K] = 0$$ Homework Equations Show that the Lie algebra for the generators ##K, P,## and ##H## is isomorphic to the...

Homework Statement The Hamiltonian of a spin 1/2 particle is given by: $$H=g\overrightarrow { S }\cdot \overrightarrow { B } $$ where ##\overrightarrow { S }=\hbar \overrightarrow{\sigma }/2## is the spin operator and ##\overrightarrow { B }## is an external magnetic field. 1. Determine...

My question is that how does the Schrodinger equation arise from the Heisenberg equation of motion in the quantum field formalism. These are from Hatfield's book. So I'm having some difficulties to reproduce (2.36) by plugging (2.55) into (2.37) primarily because H is an integral...

I may be getting these Thread Levels wrong. I get the impression that they apply to my level of knowledge such that someone else might be able to give an answer that I might be able to understand rather than the level of knowledge required to answer the question. Rest assured I am quite stupid...

When we look at those pictures of colliding particles in particle colliders, we see a large collection of curves and lines radiating out from the point of collision, representing the new particles which have been created. So two questions about this: 1) Why are these acting like particles in...

I studied only half a semester of quantum physics in high school (which i only finished 8 months ago and came first in physics luckily) but i remember Heisenberg's uncertainty principle. All over youtube people were saying things like "this is God's way of keeping us from getting into perfection...

I'm trying to understand the rotations of rigid diatomic molecules such as HCl. My understanding of the orbital angular momentum is that it is quantized with a total value equal to $$E=\frac{\hbar^2}{2I}J(J+1)$$ where I is the rotational moment of inertia and J is the quantum number. Also, J...

To my understanding(correct me if I am wrong), one consequence of the Heisenberg Uncertainty Principle is that energy levels can fluctuate by some amount, e, for a short time, t. As long as e x t does not exceed h/4pi (where h= Planck's constant). My quarry is that what are the units for the...

Hey, I have a simple question: What is the effect of the homogeneous and non-homogeneous static magnetic field in the Heisenberg spin system? Like what is so difference between the homogeneous and non-homogeneous magnetic field and what is the effects of the two cases in the spin system...

When looking at a night light with almost closed eyes, I notice that the light becomes a vertical line. When tilting my head 90 degrees, the line becomes horizontal. Can this be explained by Heisenberg's Uncertainty principle? This question has been asked in another thread : "Squinting at...

Homework Statement We consider the O2- molecule, with the Hamiltonian and position operator having matrix representations in terms of the Pauli matrices: In the Heisenberg picture, the position operator is: (1) Find the eigenvalues and eigenstates of x(t) at time t=pi*hbar/(4A) (2) The...

"historically the Heinsenberg equation of motion was first written by P. A. M Dirac, who - with his characteristic modesty- called it the Heinsenberg equation of motion." Modern quantum mechanics/ J.J. Sakurai, page 84 Why dirac did that?, I didn't find any source. Any information about this...

Homework Statement Consider a spin ##\frac{1}{2}## particle at rest in a B-field ##\vec B = B_0\vec e_z##. (a) Find the Heisenberg equations for ##\hat S_x## and ##\hat S_y##. (b) Obtain from the Heisenberg equations two decoupled second-order differential equations for ##\langle \hat S_x...

https://www.sciencedaily.com/releases/2017/03/170322143233.htmDate: March 22, 2017 Source: ICFO-The Institute of Photonic Sciences Summary: Researchers report the discovery of a new technique that could drastically improve the sensitivity of instruments such as magnetic resonance imagers (MRIs)...

Are there fundamental limits on the accuracy for measuring both position ##q## at time ##t## and momentum ##p## at time ##t+\Delta t##, with tiny ##\Delta t##? If yes, why? If no, why can't one then measure (in principle) both ##q## and ##p## arbitrarily well at the same time ##p## (which is...

Hi, I read a chapter about the Heisenberg-model, and then something about the Hubbard-Model. The Heisenberg-model just shows, that neighbouring spins allign antiparallel if J<0. The Hubbard-Model says, that there is a hopping probability t and an Coulomb replsion, so that a material becomes...

Sorry about the pun, I just couldn't resist." The amount of cocaine found in the bag Frampton was carrying was 1,980 grams. When asked why he’d been making this calculation, Frampton said: “My mind works in a strange way.”...

Homework Statement A proton is known to lie within the nucleus of a gold atom. The radius of a gold nucleus is approximately 6 fm. What is the minimum uncertainty in the proton’s velocity [you may treat the problem as one-dimensional and you should express your answer as a fraction of c]...

I'm currently designing an experiment on Double slits for a high school science fair, but I'm not sure whether it's plausible or not. I'll be spending some of my savings for this, that's why I would like to hear some feedback from more-knowledgeable people first. In this experiment, I am trying...

Preface: As I understand it, according to quantum mechanics, there is a very good probability that I am sitting right in my chair right now, typing this question out. However, there is a non-zero, ever so small probability, however infinitesimally small chance that I am somewhere else in the...

Homework Statement An electron is moving in a parallel beam along the x-direction with momentum, p=mv. It encounters a slit of width w. Assuming that the electron gets diffracted somewhere within the central maximum of small angular magnitude Δθ, estimate the uncertainty Δp in its momentum...

I'm really interested in quantum theory and would like to learn all that I can about it. I'm looking books for learning quantum physics that contains derivation of Heisenberg uncertainty principle, dirac notation, pauli matrices, quantum operators, hawking radiation, etc. What are good books to...

Hi all, I am 18 years old, and am looking to go into engineering, but I have a strong interest in theoretical physics. As such I have recently written a short research paper into the Heisenberg Uncertainty Principle, and I wondered if anyone would be willing to have a quick read and give me any...

Can anybody give a natural interpretation of operators and states in the Heisenberg Picture? When I imagine particles flying through space, it seems that the properties of the particles are changing, rather than the position property itself. Is there any way I should be thinking about these...

I've been pre-occupied with Heisenberg's uncertainty principle for around four years now, and I've come to fabricate a lot of questions. The most pressing one, however, is as follows: To me, the uncertainty principle seems to reference our (relatively) poorly controlled methods to measure a...

Heisenberg model of ferromagnet is defined by \hat{H}=-J \sum_{\langle i,j \rangle} \vec{S}_i \cdot \vec{S}_j where ##J>0## and summation is between nearest neighbours. Hamiltonian is perfectly rotational symmetric. However, the ground state “spontaneously” chooses a particular orientation...

That doesn't follow. Selecting a system to study is necessary for most of physics. But it is always a subjective act - since Nature isn't divided into system and the rest of the universe. Most of the time we don't want to consider the universe as a whole but only the particles in a particular...

Suppose we have an elementary double-slit experiment: A laser fires individual photons through a double slit at a detectionscreen made of atoms. As we fire photons, an interference pattern emerges, exposing the momentum of the photons (the frequency of the laser). So, we have registration of...

Is the Hamiltonian matrix that is constructed in Ch 8 of the Feynman lectures the Heisenberg matrix picture, or is it something else? I am just curious. Thanks, Chris Maness

In another thread, stevendaryl and I were trying to understand whether MWI can be formulated in the Heisenberg picture. Since neither of us really understands MWI, I tried to retreat to safer ground by asking: Can decoherence be formulated in the Heisenberg picture?

I would like to ask a quick (I suppose) question. Does a photon have definite energy in Heisenberg picture? My motivation for this question comes from reading that Hamitonian is generator of time evolution. But in Heisenberg picture time evolution is associated with operator not quantum system...

Dear PF Forum, Determinism. 1. Is there determinism? 2. Because we can't measure the electron position, it doesn't mean there's no determinism? Heisenberg uncertainity principle states, per wiki: But because we can't measure it, it doesn't mean that the universe itself is indeterministic...

What is the relation between "superposition" and "the Heisenberg uncertainty relation"?

I've uploaded a proof of the Heisenberg uncertainty principle from Konishi's QM. I just don't quite understand one part: what is the significance of the discriminant being less than or equal to 0? Wouldn't this just result in ## \alpha = R \pm iZ ##? Why would this be desired in this proof?

I'm a bit confused as to what is meant by instantaneous eigenstates in the Heisenberg picture. Does it simply mean that if vectors in the corresponding Hilbert space are eigenstates of some operator, then they won't necessarily be so for all times ##t##, the eigenstates of the operator will...

I understand this topic has been brought up before, however there appears to be "truth" or "lies" and very little in between when it comes to explaining the Heisenberg Uncertainty Principle (HUP) to students of freshman chemistry. I'm teaching university general chemistry to students who've had...

Multiple_Authors submitted a new PF Insights post Does the Heisenberg Uncertainty Principle Imply Energy Nonconservation? Continue reading the Original PF Insights Post.

Now after applying and removal magnetic field H=0 there will be residual magnetic domain in XYZ directions Is the Heisenberg Model at very low temperature express about the energy of the system with higher accuracy than Ising Model in the previous case ? and at high temperature is the Ising...

Homework Statement I don't get how you can use x and p instead of delta x and p in Heisenberg's principle. Also why is it just h bar? Isn't it supposed to be h bar/2? Problem 2-iv Homework Equations delta x* delta p >= h bar/2 The Attempt at a Solution I tried to deal with this problem but I...

ZapperZ submitted a new PF Insights post Misconception of the Heisenberg Uncertainty Principle Continue reading the Original PF Insights Post.

I read this article by Hawking which includes this quote " In classical mechanics one can predict the results of measuring both the position and the velocity of a particle. In quantum mechanics the uncertainty principle says that only one of these measurements can be predicted; the ob server can...

Homework Statement Show that ## \Delta\lambda\Delta\ x>lamdba^2/4*pi## The Attempt at a Solution When I substitute de Broglie's p=h/lambda I get the equation of ##\frac {\Delta\x}{\Delta\lambda} > 1/(4*pi )##

I found these two examples in a books which demonstrate Heiseberg's uncertainty relation...

I am having some trouble understanding what to use for the uncertainties in the Heisenberg principle. My chemistry book has two problems on this principle. One asks to find the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known within +- 1.0 mm/s. The...

Homework Statement Find the minimum uncertainty of the momentum of a small particle with mass m=1g, which is confined within a region of width a=1cm. Homework Equations Delta(p)*Delta(x)>=hbar/2 The Attempt at a Solution Delta(p)*Delta(x)=hbar/2 Delta(p)*10^(-2)=hbar/2 Delta(p)=10^2*hbar/2...

I was always a bit puzzled by the Heisenberg picture (not mathematically, I'm fine with that, but conceptually) - if a "state" describes a system, how can it not be time-dependent, if the system changes? I just found an alternative way of looking at it which seems to make sense to me, but I'm...

Can the Heisenberg's Gamma Ray Microscope thought experiment derive the Uncertainty Principle precisely? Most derivations I find, the uncertainty is roughly 2h, whereas the uncertainty principle is "hbar over 2". Is there anywhere where there is more precise calculations to obtain "hbar over 2"...

Homework Statement A parallel beam of electrons traveling in x- direction falls on a slit of width d. If after passing the slit, an electron acquires momentum py in the y direction then for a majority of electrons passing through the slit A. |py|d ≈ h B. A. |py|d > h C. |py|d < h D. |py|d >> h...

For the harmonic oscillator in 1-D we get the 2nd time derivative of the x Heisenberg operator = -ω2 x. When that is integrated it gives xH (t) = Acos(ω t) +Bsin (ω t) where A and B are time independent operators. My question is why are the constants A and B incorporated into the terms as a...

Hi, I'm completely stuck with problem 3a). I have no idea of how to start. Anyone have any clue?http://speedy.sh/9JkCf/handin1-4.pdf