Heisenberg Definition and 311 Threads

Homework Statement A beam of 50eV electrons travel towards a slit of width 6 micro metres. The diffraction pattern is observed on a screen 2m away. Use the angular spread of the central diffraction pattern (+/- lambda / slit width) to estimate the uncertainty in the y-component of momentum...

Homework Statement Find density of states H = \frac{-JzM}{g\mu_B} \sum_i S_i^z + \frac{JzNM^2}{2g^2\mu_b^2} = -\alpha \sum_i S_i^z + \gamma[/itex] z = # nearest neighbors J = exchange M = magnetization S^z = project of total spin S=0,1. Homework Equations Z=\sum_{S m_s} <S m_s| \exp(-\beta...

Hi, I've just worked through a derivation of the H.U.P. that uses the Cauchy Schwarz inequality to come up with the expression (\Delta A)^2(\Delta B)^2 \geq \frac{1}{4}|<[A,B]>|^2 . This much I am happy with, but then it seems that when dealing with two "canonically conjugate observables" you...

Hi! So I know what the Uncertainty principle states and everything, but I can't find anywhere the "causes" of the uncertainty. Like, what is it exactly that "causes" the uncertainty. If it's not the measurement tools/technology, then what is it?? Please explain in terms of physical phenomena...

given 2 unnormalized wave functions: Y1(x)=e^i(x/m) Y2(x)=1/2*[e^2i(x/m) + e^3i(x/m) + e^-2i(x/m) + e^-3i(x/m)] if the positions of the particles were measured, which would be found to be more localized in space? (that is, which has a position known more precisely?) to my...

On the Wikipedia page for http://en.wikipedia.org/wiki/Heisenberg_picture#Mathematical_details" we find this relation \frac{d}{dt}A(t)=\frac{i}{\hbar}[H,A(t)]+\left(\frac{\partial A}{\partial t}\right) I don't understand what the distinction between \frac{d}{dt}A(t) and...

Why do we get line spectra from absorption/emission of atoms, but band spectra from absorption/emission of molecules? As I understand the Heisenberg Uncertainty Principle mathematically, some operators do not commute and as such, the order of measurements determines the results. In regard...

Does the uncertainty principle apply only to electrons or other particles as well?

Hi, I am trying to teach myself some quantum mechanics and here is something I am stuck on. Various derivations of Heisenberg uncertainty start out with two Hermitian operators, usually called A and B to represent position and momentum. Then they define another two operators ∆A and ∆B as...

First, I'm not sure where this fits (here or Quantum Mechanics), because it's completely in-between the two... Is there a way to account for the fundamental uncertainty in quantum mechanics through a modification of general relativity? I have very limited experience in Quantum mechanics, and...

I wonder if Heisenberg principle (both \Delta p \Delta x \geq \frac{\hbar }{2} and \Delta E \Delta t \geq \frac{\hbar }{2}) can be applied to photons. Say I have a laser emitting a flash. I know very well the wavelength of the photon, therefore its momentum. Also, I know well where it might...

Homework Statement One could imagine that beta decay was due to a electron initially inside the nucleus and than leaving it. Proof by using Heisenberg uncertainty principle that this is not possible. There is a hint which says you can use energy spectra and values for the energy of beta...

Hi All, I am trying to remember the logical argument that leads from Heisenberg's uncertainty principle to the existence of quantum superposition states. Here's my sketchy version: 1) postulate of Quantization leads to non-commuting operators 2) This leads to Heisenberg Unc. Principle...

\Delta E \Delta t \geq \frac{\hbar}{2}. If I understand well, if I measure the energy of a particle (or system of particles) with a great precision, I cannot know well at all when the system had this energy... right? My doubt is: The system had (or will have?!) the energy I measured, but when...

\Delta x \Delta p \geq \frac{\hbar}{2}. Say I want to measure the best I can the position of an electron, in detriment of its momentum (i.e. velocity since I assume that I know its mass quite well). When \Delta x \to 0, \Delta p should tend to +\infty but there's the c limit so that I can't...

I was trying to follow http://www.youtube.com/watch?v=dCua1R9VIiQ&p=EFD655A9E0B979B7&playnext=1&index=54" lecture at the 4:15 mark but am having a little difficulty. In particular, why doesn't he have to take the commutator of all four of the terms you get when you square (p-eA). Is he using...

Homework Statement hi i am new to this principle if i was to calculate the Heisenberg uncertainty of a nuclei of radius r would i take my delta x as r or as the diameter of the nuclei thanks Homework Equations The Attempt at a Solution

Hi, this is my question: suppose that at time t' our system is in the state | \psi(t')\rangle The probability for the system to be in the state | \phi\rangle at the time t'' is the norm of \langle \phi| \psi(t'')\rangle This in the Schrodinger picture. But how i can write the same thing in...

Please tell me where my understanding of the Heisenberg and/or the Schrodinger picture falls apart. -Schrodinger says the state vector of a system changes with time according to a unitary operator that doesn't change with time. -Hesienberg says the state vector of a system doesn't change...

Hello, I'm studying the Heisenberg Model. Given the Hamiltonian H = - 2 \frac{J}{\hbar^2} \vec{S}_1 \vec{S}_2 with \begin{equation} \vec{S} = \frac{\hbar}{2} \; \left( \begin{array}{ccc} \sigma_x \\ \sigma_y \\ \sigma_z \end{array} \right) \end{equation} \sigma_{x,y,z} \quad...

In Six Easy Pieces: Fundamentals of Physics by Feynman, the claim is made that the reason why electrons don't just collide “ontop” of the nucleus is due to the Heisenberg uncertainty principle. This perplexes me greatly; it sounds wrong to me. The moon and the Earth do not collide because...

There are two basic facts that I have difficulty reconciling: (a) the magnetic and electrical components make up a complementary pair of variables (b) Maxwell's equations describe the magnetic component in terms of the electrical one and vice-versa My question is definitely not original...

From what I understand, the Heisenberg Uncertainty Principle means that we can never know the position and velocity of a particle at the same time, as the measurement of one necessarily affects the measurement of the other. Great. I understand that theory, and it makes perfect sense. But what...

I got in an argument with my dad over the weekend. Is the Heisenberg uncertainty principle a result of technological limitation or a basic premise in quantum mechanics? Basically is the information fundamentally "unknowable" or simply unmeasurable?

Heisenberg Uncertainty, Need Some Clarification. TIME SESITIVE, HELP! Homework Statement Use the Heisenberg uncertainty principle to calculate Deltax for a ball (mass = 100 g, diameter = 6.65 cm) with Deltav = 0.645 m/s. Homework Equations PX = h/(4*3.14) The Attempt at a Solution...

Homework Statement Starting from one of the more familiar Heisenberg Uncertainty Relations, derive the Uncertainty Relation involving angular momentum and angular displacement and explain its significance. Homework Equations The relevant uncertainty relationship is that between...

Homework Statement 18. A ball of mass 50 g moves with a speed of 30 m/s. If its speed is measured to an accuracy of 0.1%, what is the minimum uncertainty in its position? 19. A proton has a kinetic energy of 1.0 MeV. If its momentum is measured with an uncertainty of 5.0%, what is the...

After about 20 years I'm going back and brushing up on quantum. I am confused about an electron in an s-orbital having zero angular momentum as well as how angular momentum in general relates to Heisenberg uncertainty. I probably have a few misconceptions as well as missing some key pieces...

Scientists have reportedly been able to transport atoms and molecules as much as 1800 feet. Could the same be done for humans, or would the Heisenberg Uncertainty Principle ultimately make it impossible?

Hey guys, I ran some simulation of thermal phase transition of three dimensional quantum antiferomagnetic cubic lattice. I'm pretty happy with critical temperature, but I'm not sure about critical exponents because I'm having trouble locating some reference with their best known values. I know...

Hi All, I understand that it is impossible for man to know both the position and momentum of a particle with arbitrary accuracy. This is a result of the physics of photons which are necessary to observe an object. Now although man cannot know the exact position and momentum...

Is the Heisenberg Uncertainty Principle as statement about the state of a particle or only a statement about what can be observed about a particle?

a 1.0 micrometer diameter dust particles (mass 1.0x10^-15kg) in a vacuum chamber pass through a hole (diameter assumed to be exactly that of particle) onto a detection plate 1.0m below. By how much does the diameter of the circle increase Homework Equations This is clearly a Heisenberg...

What is approximation of the chaotic phases for Heisenberg feromagnet in low temperatures?

Hi, I have a problem with the uncertainty principle. The way I understand it, Heisenberg used ideas from classical mechanics and the concept of wave/particle duality to show a contradiction in classical mechanics, i.e. that it is impossible to know with exact precision both the momentum and...

I read that the Heisenberg uncertainty principle arises for stuff like electrons simply because the observer affects the observed . That is,because photons (or what ever the observer uses to detect the position) will affect the trajectory of the particle... That doesn't make much sense to...

So, I'm doing some undergraduate research in quantum spin systems, looking at the ground states of the Heisenberg Hamiltonian, H=\sum{J_{ij}\textbf{S}_{i}\textbf{S}_{j}}. But I think I have a critical misunderstanding of some fundamental quantum mechanics concepts. (I'm a math major, only had...

Sorry about not using symbols but I haven't learned how to do that yet. 1. Homework Statement A woman is on a ladder of height H. She drops small rocks of mass m toward a point target on the floor. Show that according to the Heisenberg Uncertainty Principle, the average miss distance...

Hi everybody! I'm looking for the critical exponent ν (i.e. the one of the correlation length) of the Heisenberg (i.e. equal coupling in all directions) antiferromagnetic spin-1/2 model in 1D... Furthermore, do you know to which universality class it belongs? Is it true that it's the...

if we can find a 'soliton' solution for Nonlinear Schroedinguer equation , then does this imply that Uncertainty principle is false ?? since a soliton is a localized wave packet then i can find the position of the soliton and its momentum so apparently i have violated uncertainty.

Hello all I have a question concerning The Heisenberg Uncertainty Principle. The principle mathematically looks like this- \Delta x\Delta p \geq \hbar/2 The principle states that you can not measure more than two quantities simultaneously. If you know a...

hi folks, last problem I can't get done here. I usually have a good idea of where to start, what to use. but I'm a bit flummoxed. Homework Statement A neutron, of mass m = 1.67 10-27 kg, is localized inside a carbon nucleus, of radius 7.0 fm (1 fm 10-15 m). Use the uncertainty relations...

Homework Statement Sort of stuck deriving the Klein-Gordon equation from Heisenberg equation of motion \dot{\varphi} = i [H, \varphi ] Homework Equations \dot{\varphi} = \frac{\partial\varphi}{\partial t} H = \int d^3x \mathcal{H} \Pi (x) = \dot{\varphi}(x) \mathcal{H} = \Pi...

Homework Statement Using the uncertainty relation for momentum and position, show that the quantum-mechanical uncertainty in the position of a particle at temperture T is \Delta x~\sqrt{\frac{h^{2}}{4mkT}} where T is the temperature and k is the Boltzmann's constant. Homework Equations...

Just reading about how if an operator commutes with the Hamiltonian of the system then its corresponding obserable will be a conserved quantity. my notes say that if \hat{L} commutes with the hamiltonian then the angular momentum will be conserved. this kind of makes sense but surely it's...

Homework Statement Particles pass through a single slit of width 0.2 mm in a diffraction setup. The de Broglie wavelength of each particle is 633 nm. After the particles pass through the slit, they spread out over a range of angles. Use the Heisenberg uncertainty principle to determine the...

HUP states that "certain physical quantities, like the position and momentum, cannot both have precise values at the same time. The narrower the probability distribution for one, the wider it is for the other." (Wikipedia) I am not a physicist, but I have been pondering this question: In this...

Wich are the differences between the theorem of ehrenfest and the Heisenberg's rappresentation of quantum mechanics?

Can anyone prove, in layman terms (or as close an approximation to layman terms as is possible), why exactly ∆p ∆x ≥ h-bar /2 ? Please explain every step in the deduction, and not just with formulae. I can't just take something for granted. Thanks in advance.

Amazing British documentary. :!) BBC - The Copenhagen Fall Out In World War II, there were mounting fears that Hitler was building an atomic bomb. Such a prospect depended on two of the world's top nuclear scientists; brilliant German physicist Werner Heisenberg, and his Danish mentor, Niels...