Uncertainty Definition and 1000 Threads

Ok hey forum. I thought it might be a neat idea to contemplate this idea, and perhaps regurgitate some thoughts back on to this thread. So, as the Heisenberg uncertainty principle states, one can not know both the velocity and position of a particle or electron. I was curious to hear thoughts...

does the epsilon delta definition of the limit connect to the uncertainty in measurements like this? like if we measure a quantity time with value a with error of + or - delta then my formula will give me v with value L +or - epsilon or is it unrelated?

Homework Statement N=a^+a a=\frac{ip+mwx}{\sqrt{2m\hbar w}} \quad a^+=\frac{-ip+mwx}{\sqrt{2m\hbar w}} |z>=e^{\frac{-|z|^2}{2}}\sum^{\infty}_{n=0}\frac{z^n}{\sqrt{n!}}|n> where <n|n>=1 Show that the variance (uncertainty) in N, \Delta N is |z| i.e. calculate (\Delta...

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 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...

What is the volume of the pool? 165 m^3 What is the uncertainty in the volume of the pool? Express it in terms of cubic meters. 20.6 m^3 Joe's supervisor says, "Okay, Joe, your first job is the fill the pool. We used to use a hose, but it sprang a leak. Instead, you'll have to fill...

Homework Statement i have a few results of measurements, with different measurement uncertainty: L=5\pm0,2, L=5,1\pm0,1,L=5,2\pm0,3,L=5,3\pm0,1,L=5,4\pm0,2 and how can i count standard deviation and final result of measurement with uncertainty? The Attempt at a Solution i counted arithmetic...

I was reading the book "the grand design" by stephen hawking and I reached the part about randomness and Heisenberg's uncertainty that I didn't understand. The book seems to suggest that "Probabilities in quantum theories reflect a fundamental randomness in nature". The thing seems right to me...

Hi, I am currently having problems solving a an exercise: Let's make the assumption of the existence of an operator H such as [T,H]=i \hbar I. by examining the state: |\psi\rangle}=He^{i \alpha T}|E\rangle} with H|E\rangle}=E|E\rangle} show that the spetrum of H is not bounded below.

Hi all, A question about the Holographic Principle. I've recently started reading up about this, and watched Bousso's neat introductory video . I thought, "Ah, this is so refreshingly simple!", and proceeded to write down my own notes. However here things revealed themselves to be not...

Hi, I have just managed to make a PIC light blink. My question has to do with the syntax. In my code, I use a Delay subroutine that is called in between turning the LED on and turning it off. I tried two codes. The first had my Delay subroutine being placed before my main code. The second had...

I'm trying to decide on a method for calculating a weighted mean for my data. In Bevington's Data Reduction and Error Analysis for the Physical Sciences 2nd Ed. Equation 4.19, the variance of the weighted mean is: However, Bevington also suggests the use of Equation 4.22 substituted...

Okay I actually have 2 questions. 1) ΔxΔp >= h / 2π Is x one dimensional? Say if I wanted to locate the certainty of an electron in a hydrogen atom with a diameter of 10e-10 m. The electron is confined to the volume of the atom, not just the diameter, so could I say Δx = 10e-10 or...

hi, I do wonder if the Higgs boson is a quantum object because since it is the (only) particle with spin 0, then it should not behave like a wave(since the wave aspect is connected to the fact that it is spinning) and therefore not experience the uncertainty principle. Or am I wrong?

Homework Statement See q attached Homework Equations The Attempt at a Solution Am i right in thinking that the answer to both questions is yes? Neither of the commutators [p, V(x)] nor [x, H = + or - ih.. therefore is the answer to both a and b yes?

HI, I will not used the template provided since this is not a textbook problem. It's a problem I have with a demonstration in Quantum Mechanics Vol 1, Cohen-Tannoudji " Complement C III [Q,P] = i \hbar Consider the ket: |\phi \rangle = (Q +i\lambda P)|\psi \rangle where \lambda is an...

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...

Homework Statement A metal bar has a length measured to a precision of +-1%, a mass measured to +-2% and a radius masured to +-3%. What would be the % error in the value of the density of the metal in the bar calculated from these? Homework Equations V=(pi)r^2h D=m/v The Attempt at...

Homework Statement http://img219.imageshack.us/img219/306/prblem.png (oops, that line should end with "just before measurement? (Express your answer in terms of the variances of the two operators)" ) The Attempt at a Solution...

Homework Statement I currently want to add 2 percent each with a relative uncertainty together: \frac{53.3\% +/- 1\% + 65.8\% +/- 1\%}{2} I'm not sure how I can add the percentage uncertainty. Homework Equations The Attempt at a Solution I've concluded that the average is...

Hello community. My second stupid question. In the book by Nouredine Zettili , the uncertaintie operators are defined as \DeltaA = A - <A>, where A is an operator, and <A> = <\psi|A|\psi> , with repect to a normalized state vector |\psi> i was wondering, why is not the uncertainty...

In the Messenger Lectures (http://research.microsoft.com/apps/tools/tuva/index.html) Feynman says that the theory of "hidden variables" tells us that the cause of uncertainty in nature (the cause that nature works with probabilities) is that we don't have enough information to predict the...

\Delta{x}\Delta{p}, \Delta{E}\Delta{t} and particle spin all have units of angular momentum and have ability to be quit uncertain... Any idea if they have something in common (except the units of measurement)?

hi, in the position momentum uncertainty principe , should we believe there is an uncertainty about the mass and not only about the velocity? thank you very much for your reply!

After measurements, the following values and their uncertainties were recorded: x = 8.3 ± 0.1 and y = 2.72 ± 0.07 Find the following values of Z a) Z = x + y b) Z = x - y c) Z = xy d) Z = x/y e) Z = y/[(x)^0.5] (this is y divided by the square root of x) f) Z = exp(y)...

Hello, I'm (only) receiving an introduction to Quantum Physics atm, and today our professor argued that the uncertainty principle doesn't have a definite form: the right hand side of the inequality is dependent on the confidence measure/certainty you choose, in other words 95%, 99% certainty...

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...

From the wikipedia page on http://en.wikipedia.org/wiki/Complementarity_(physics)" : As I recently noticed in the double-slit experiment there is a lot of time-uncertainty, not only position-momentum uncertainty. That is shown in the fact that the probability wave does not reach the screen...

Homework Statement If you were to measure ten identical measurements, would that imply that your measurement of the wavelength had no uncertainty? what would the uncertainty of the measurement be in that case? Homework Equations n/a The Attempt at a Solution I am thinking no...

in what scale can we consider the uncertainty principle?can it be considered in the non atomic scale?

Show that for a free particle the uncertainty relation can be written as (Delta lambda) (Delta x) >= lambda^2 / 4pi Firstly I am sorry not writing this in latex but I gave up after trying to write it in latex for half an hour. Would be great if anyone can show me how to do it. Using...

Homework Statement Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values...

Since we know the precise velocity of any photon, does that mean it's location is always undeterminable?

Homework Statement My first lab report in physics requires me to calculate the value of local gravity. I did this using latitude and longitude. I must also state the uncertainty of my local gravity value. I have no clue how to do this. What am I basing my uncertainty on, and is there an...

Homework Statement Imagine that you are driving down a stretch of freeway with a posted speed limit of 65 miles per hour. You aren’t sure whether to trust your speedometer, so you check your speed against a series of distance markers along the interstate. You notice that, in the time it takes...

Homework Statement Calculate the following, expressing all results with uncertainties both in absolute and relative (percentage) form: a) A + B b) A x B c) Asin(theta) d) A^2 / Bcos(theta) The relevant formula for the absolute uncertainty is below, but i have no idea how to...

Hi, I have taken an introductory undergraduate QM course, solving for different boundary conditions like particle in a box, but the physical interpretations of some of the tenets was not well explained. I was surprised to find this paragraph on Wikipedia: "Published by Werner Heisenberg in...

Homework Statement The radius of a circle is measured to be 14.3+-0.3cm. Find the circle's area and the uncertainty in the area. I don't understand how to correctly apply uncertainty equations with sigma and partial derivatives to these types of problems. Homework Equations...

Homework Statement Show that the smallest possible uncertainty in the position of an electron whose speed is given by \beta = v/c is \Delta x_{min} = \frac{h}{4 \pi m_0 c}\sqrt{1-\beta^2} The Attempt at a Solution Since \Delta x \Delta p \geq \frac{\hbar}{2} , we see that \Delta x_{min}...

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

Hello everyone. I need your help. I am not a physicist or a physics student, so I am not familiar with the subtleties of quantum mechanics. I do have a good general education, though, and I am eager to learn new things. I have long had a problem with quantum mechanics, specifically the...

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...

Homework Statement Find the Uncertainty Measurement using Precision Error and Bias Error? The Length of line is 5.625 in. Precision Error is 0.13 in. Bias Error is -0.115 in. What is the UNCERTAINTY measurement? Homework Equations None. The Attempt at a Solution Please help! I...

Hi people. I am a bit confused about the uncertainty principle. According to Heisenberg, we cannot exactly determine the position and momentum of an electron at the same time because the minimum energy we have to give out (say light energy) is absorbed by the electron and one of the quantities...

I am a little confused by something by something in my physical chemistry textbook. If two measurable quantities do not commute, then an uncertainty relation exists for them. Kinetic energy and position do not commute, and the expectation value for linear momentum in a 1-D particle in a box...

1. this is for a particle in a box (infinite potential well): For the wave functions calculate (as a function of n) \Deltax \Deltap \Deltax\Deltap Homework Equations h = h bar below u+n(x)=(1/\sqrt{a} )cos((n-1/2)(pi)x/a) u-n(x)=(1/sqrt{a})sin(n(pi)x/a) E-n=h2/(2m)(n(pi)/a)2...

A particle is confined within a spherical radius of one femtometer(10^-15 m)? Its momentum can be expected to be about- 1. 20 keV/c 2. 200 keV/c 3. 200 MeV/c 4. 2 GeV/c How should I go about using HUP on a problem like this one? I tried substituting x=10^-15 meters in px=h/4 pi but the answer...

Homework Statement How do we solve this problem? % Difference = (l 0.282 +/- 0.0019 - 0.288 +/- 0.04 l) / 0.285 +/- 0.02 Homework Equations Percent Difference = (l value - average value l)...

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...