Heisenberg Definition and 290 Threads

Ground State Wave Equation: ψ0=(a/∏)(1/4)e(-ax2/2) Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values. First I found <x>=0 because it was an odd function then I found <Px>=0 because it was an odd function Then <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of...

hi friends. i don't know how can i write a fortran code for expressing spins in Heisenberg model which have 3 dimension spin operator, sx,sy,sz? thanks for your help

Why is minus sine in definition of hamiltonian H=-\sum_{i,j}J_{i,j}(S_{i}^+S_{j}^-+S_i^zS_j^z) Why not? H=\sum_{i,j}J_{i,j}(S_{i}^+S_{j}^-+S_i^zS_j^z)

General Relatitivity predicts Timelike curves and there are nonlinear extensions of mechanics which resolve the paradoxical aspects of CTC's *i.e. Time Travel, on the other hand Hawking proposed a conjeture to rule out CTCs, the Chronology Protection Conjecture* there are a class of Timelike...

I knew that Heisenberg did not emigrate when the Nazis took power, but I was shocked to learn that he tried to help the Nazis get the atom bomb. This is textbook irrationality. Here's one example of irrational behavior. 1. You want A 2. B prevents the acquisition of A 3. You do B 4...

Im sorry, I accidently edited my opening post instead of posting a new one.. The question was regarding the statement that the state ket is stationary in the Heisenberg picture when the basis kets are transforming in time. Because the state ket is a superposition of the base kets it should the...

Homework Statement This is not a problem as such. Just a derivation for which I've been given a solution which I cannot seem to find. Homework Equations Ke = 1/2 mv2 = ρ2/2m hbar << 2ΔxΔp Δp≈p as the average magnitude of p is small. The Attempt at a Solution p >> hbar/2Δx p2...

Homework Statement Assume speed of 435g football is known with 1mm/s uncertainty. What is the minimum uncertainty in its position? Homework Equations I'm not quite sure... I know p=mv, and I know that Heisenberg's uncertainty principle states that certain parameters of quantum...

How do we know that the uncertainty principle is a property of an electron and not a limit of our measuring ability? I understand that photons striking an electron alter its momentum, but imagine an electron that is not being observed. Couldn't it have both a position and a momentum at a given...

The general definition is that we cannot determine the location and velocity of a particle at any given moment. However, my intuition is to assume this is due to shortcomings in technology and measurement, but apparently that's false. This is a rule of nature. Can you explain what exactly the...

I would like to find out how popular is Heisenberg picture. Is there someone who finds Heisenberg picture useful? And as well - are there any ideas how photon double-slit should be treated in Heisenberg picture?

Hey Given an anisotropic hamiltonian \mathcal{H} = -\sum_{j,\rho} \left( J_\rho^z s_j^z s_{j+\rho}^z + \frac{J_\rho^{xy}}{2}\left( s_j^+ s_{j+\rho}^- + s_j^- s_{j+\rho}^+ \right)\right) - g\mu_B H\sum_j s_j^z Here \rho is a vector connecting the neighbouring sites. How do I show that the...

Where How did he come up with that?

Does anyone know of a COMPLETE derivation of the Hubbard Model and then the Heisenberg model from it. What I mean by complete is pedagogical including all (or at least most) steps. Books like Assa Auerbach's and Altland and Simons are worthless for these kind of things (in fact IMHO those...

From what I've gathered reading the scientific literature, the more precise we know a quantum system's position, the more uncertain the momentum becomes. Does the uncertainty principle place a limit on how well we can know a system's position when we measure that observable? I've read...

Hi there, So here's my assignment: ''The velocity of a positron is measured to be: vx=(4.00±0.18)*105 m/s, vy=(0.34±0.12)*105 m/s, vz=(1.41±0.08)*105 m/s. Within what minimum volume was the positron located at the moment the measurement was carried out?'' I think I'm not wrong when I say that...

Hello, I'm studying superconductors and I began to wonder about Abrikosov vortices. They possesses a precise quantum flux (h/e), and are also localized in space enough to be exactly pin-pointed by experimental techniques. As it is some kind of a quantum object, shouldn't these vortex properties...

Homework Statement Consider a particle in a one dimensional box of length L, whose potential energy is V(x)=0 for 0<x<L, and infinite otherwise.Given the wave function at ground state ψ=sqrt(2/L)sin (pi*x/L) Compute ΔxΔp where Homework Equations Δx=sqrt(<x^2>-<x>^2) and...

I don't want to name him explicitly, in fear of blemishing his name in case he is not a fraud. Just google (including the ""-symbols) and the relevant wikipedia page should be the first hit. Apparently the scientist first went to a group established in 1975, and afterwards he went to work...

No object can travel faster than the speed of light, so it would appear evident that the uncertainty in the speed of any object is at most 3 * 10^8 m s (a) What is the minimum uncertainty in the position of an electron, given that we know nothing about its speed except that it is slower...

Let me first start off by saying that I am somewhat new to physics and it's understanding. But I was looking over the Hiesenberg Uncertainty Princple and a thought occurred to me. The Heisenberg Unvertainty Principle states "More precisely the position is determined, the less precise the...

Homework Statement I've seen this example for using the Heisenberg equation of motion to solve the Simple Hamonic Oscillator. http://en.wikipedia.org/wiki/Heisenberg_picture#Commutator_relations" However, if you were only interested in one variable, let's say position, on how the the...

Hello I know this topic must have been done to death already, but i can't seem to find a satisfying answer. As the title suggests, my question is, what experiment proves that the uncertainty principle is not just a result of our flawed measuring techniques? From what i understand, when we...

I'm trying to understand the Heisenberg Uncertainty Principle, as it relates to experimental measurements, because it's kind of confusing me. We just learned the derivations for it in my QM class -- basically it's two standard deviations multiplied together (corresponding to measurements of...

I was recently thinking about the Heisenberg Uncertainty Principle which states that we can not know a subatomic particle's position and momentum at any instant. We can know one or the other measure but not both at the same time. The more we know about one, the less we know about the other...

Homework Statement You have a latice of particles that all have spin 1, but they can change the direction of their spin so constraint \left|S_j\right|=1. There is only interaction with the closest neighbours so we have the following hamiltonian: H = -J \sum_{\left\langle ij \right\rangle}...

Am I right in thinking that the Heisenberg matrix interpretation describes emission, while the Schroedinger interpretation does not?

i am not getting the interconnection between probability wave function of particle with particle's momentum,can anyone help? i don't want any mathematical equations,any theoretical explanation would suffice

It is stated that electrons orbit the nuclei of atoms not as particles. By the Heisenberg Uncertainty Principle (whatever that is) one cannot pinpoint their actual location and one cannot track the motion of an electron as it orbits the nucleus. What is that all about? Please use 10th...

I am new, and I don't have a physics background, so please excuse the question if it is incredibly easy... Does the Heisenberg Uncertainty Principle mean that we just can't measure the location of an electron to perfect accuracy, but such a location does exit (we just can't know what it is)...

So to determine the position of an object you can scatter light off of it. Fine. But then my textbook says you can't know the exact position of the object because of diffraction effects. We've covered the diffraction of light through narrow slits but I don't know why if you were scattering light...

Homework Statement Modern electron microscopes used in biological research emit a beam of electrons with a velocity of 1.5x108 m/s a. What is the wavelength of an electron in the beam? b. The wavelength of the particle determines the resolution of the microscopy. Assume that you desire a...

Is it true that "The dogmas of relativity theory cannot be expected to apply to the consideration of the dynamical process by which reality actually unfolds."?? What does it mean? Physicist Stapp was describing about the Heisenberg ontology and it's possible relativity problem:

　 We know Copenhagen settles for computational rules connecting human observations rather than striving to comprehend the nature of the underlying reality. Heisenberg eventually did try to form a coherence picture of what is actually happening. But how come this Heisenberg Interpretation is not...

Homework Statement \phi(x) is in Schwartz space, and {\int|\phi(x)|^2dx=1. I need to show that (\int_{R^n}|x|^2|\phi(x)|^2dx)(\int_{R^n}|\xi|^2|\phi(\xi)|^2d\xi)\geq \dfrac{n^2}{16\pi^2}Homework Equations Heisenberg uncertainty in one dimension...

I have a question. What is the definition of Heisenberg hamiltonian? \hat{H}=-\sum_{i,j}J_{i,j}\hat{\bfs{S}}_i\cdot \hat{\bfs{S}}_j or \hat{H}=-2\sum_{i,j}J_{i,j}\hat{\bfs{S}}_i\cdot \hat{\bfs{S}}_j or \hat{H}=\sum_{i,j}J_{i,j}\hat{\bfs{S}}_i\cdot \hat{\bfs{S}}_j or...

Suppose we have time-dependent operator a(t) with the equal-time commutator [a(t),a^{\dag}(t)]=1 and in particular [a(0),a^{\dag}(0)]=1 with Hamiltonian H=\hbar \omega(a^\dag a+1/2) The Heisenberg equation of motion \frac{da}{dt}=\frac{i}{\hbar}[H,a]=-i\omega a implies...

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...

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...