Uncertainty Definition and 1000 Threads

Homework Statement Find the uncertainty of the kinetic energy of a quantum harmonic oscillator in the ground state, using \left\langle p^2_x \right\rangle = \displaystyle\frac{\hbar^2}{2a^2} and \left\langle p^4_x \right\rangle = \displaystyle\frac{3\hbar^2}{4a^2} Homework Equations...

I performed an experiment using different wavelength lasers to calculate the distance between the pits of a DVD by measuring the angles formed by the resulting diffraction pattern,but now I'm unsure on how to calculate the uncertainty of the final result. I took 9 measurements each with their...

Hi, The FAQ is a good answer, but it leaves me wondering about something. From what I read, the jist is that a short enough measurement sees no difference between an energy eigenstate and a quantum superposition which mostly comprises of that energy eigenstate but also has a few other...

Hey guys, I have a few questions I would like to ask if that is okay First off: I was doing an experiment regarding Boyle's Law, and there are some questions that accompany it. I had a syringe filled with gas and I had to add mass on the syringe so that the piston moved down. I had to convert...

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...

Homework Statement This has been bothering me for quite a while. I'm trying to work out how many measurements I will need to make to get my uncertainty under a predetermined value. If say I want the a fractional uncertainty \frac{\delta T}{T} to be equal to or under some value for some timed...

All of the statements of Heisenberg's uncertainty principle that I've read seem to state that there is a fundamental limit on the precision to which you can measure the values of conjugate pairs (like position and momentum) at the same time. So is this simultaneity necessary? I ask because...

Homework Statement Show that (\Delta A)^{2} = \langle \psi |A^{2}| \psi \rangle - \langle \psi |A| \psi \rangle ^{2}\\ \phantom{(\Delta A)^{2} }=\langle \psi | (A - \langle A \rangle )^{2} | \psi \rangle , where \Delta A is the uncertainty of an operator A and \langle A \rangle is the...

At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves ##\psi = \psi_0(k) e^{i(kx - \omega t)}## over wave numbers ##k##. We do it at ##t=0## hence ##\psi = \psi_0(k) e^{ikx}## \psi = \int\limits_{-\infty}^{+\infty} \psi_0\!(k) \cdot...

In some QFT books they say:If we consider momentum p of particle being very great,then the physics is at short scale.Then how can we apply Heizenberg uncertainty principle when the momentum p of particle having a certain value?What do they imply when they say that?

Heisenberg's uncertainty principle asserts a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously. The more you know about one, the less you know about the other. Why does the following...

Hi everyone, I have a plot of some data points that have error bars on the y axis. A bit of software I am using gives me the best fit gradient and a "Standard Error", but it doesn't take the size of error bars into consideration. I'm assuming that it just looks at how well the gradient...

Hello, I have been stuck on this prelab all day.I have finished all the questions except for the last one, where it asks you to find the uncertainty (or standard deviation) of Fave. I have tried every resource and nothing has helped so far. Any help would be great! Thanks

I'm trying to understand the uncertainty principle. ΔxΔp >= h/4∏ from my understanding of the concept, its not possible to know the value of the position and the momentum simultaneously. yet the problems that i see floating around on the internet seem to just plug in values for mass and...

A photon is considered as a quantum particle, right? However since we know the speed of a photon(speed of light) and hence can predict its position, isn't it violating the Heisenberg Uncertainty Principle? Where am I going wrong? Is it false to believe that a photon is a quantum particle?

This question may have been posted before, but I didn't have much luck finding it. We can't know the momentum and position of a particle at the same time, but if one were to entangle two particles (I.e. photons), wouldn't it be possible to measure one quality on each and thus deduce both the...

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

Greetings fellow members, I have some queries on a laughably rudimental topic regarding measurements. Say you have a metre rule with sensitivity of 0.1cm, and you are measuring a wire which stretches from the 0.0cm starting point to the middle point between 7.3 cm and 7.4cm. My...

Homework Statement I have a wire of some resistance, resistivity, and length. What is the maximum error in measuring the diameter that you can have if the resistance is to have 1% uncertainty? Homework Equations R = \frac{ρ*l}{\pi*r^{2}} for which I substituted the area as \pi(.5...

Can the Planck relation, and the Heisenberg and the time-energy uncertainty principles be derived, or produced, from the equations of General Relativity?

Finally I found the time to write my account on the interpretation of the Heisenberg uncertainty principle vs. the question whether it can be interpreted as Heisenberg did in his very first paper on the subject. Although it is well known that this interpretation is not compatible with quantum...

For two years now, I have been on PF. I spent many of those months checking PF - largely the academic and career guidance forums - just about every other day, and I learned a great deal about academia, and careers in science and engineering. A few months ago, when I posted in the Mathwonk's...

In some experiments like Heisenberg's microscope and Davisson–Germer experiment,we see that by using light to understand the actual path of electrons,the electrons are disturbed and so the result is changed(in the second case,the interference pattern is replaced by the distribution of classical...

According to this article, scientists were able to bypass the Heisenberg Uncertainty Principle, creating relative certainty in measurement of both position and momentum. Any thoughts, objections, comments?

It seems the uncertainty principle, the commutator between operators, and the symmetry of the action integral are all related. And I wonder how universal this is. For example, the action integral is invariant with respect to time, and this leads to conserved quantity of energy. This means...

Homework Statement The experiment set up is a steel ball bearing is held from an electromagnet and above a switch at the bottom. When the electromagnet is switched off a timer starts and stops when it hits the switch. The height from the bearings initial position to the switch is measured...

Homework Statement Book: Introduction to error analysis, Taylor In page 66, quick check 3.8 If you measure x = 100\pm 6, what should you report for \sqrt{x}with its uncertainty. Homework Equations Rule for uncertainty as power: \frac{∂q}{|q|} = |n|\frac{∂x}{|x|}where q = x^{n} 3...

I notice that many physicists say that virtual particle fluctuations occur in space "because Heisenberg's Uncertainty Principle allows them" Is this really the best form of reasoning? Isn't it actually the other way around - that because virtual particle fluctuations happen, then there is a...

As my knowledge of an electric field strength becomes more precise, what physical quantity becomes correspondingly less precisely known?

Consider two hermitian operators A and B. Imagine a system is in state |\psi\rangle ,then we have: \langle \psi|[A,B]|\psi\rangle=\langle \psi|AB-BA|\psi\rangle=B^{\dagger}A^{\dagger}|\psi\rangle-BA|\psi\rangle=BA|\psi\rangle-BA|\psi\rangle=0 This just seems a little strange,for example...

Why do we define the uncertainty in some physical quantity ##A## as: $$\delta A = < \sqrt{<A^2> - <A>^2} > .$$ I know that it can be derived by computing the variance of ##A##, but what is the physical meaning? Thanks!

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...

Hi, I am in the middle of a project dealing with the mass loss rate of protostars and hence I am working with the distance that these sources are away from us. I need to find the error in these distance measurements, however I cannot. In any paper (I find) that cites distances it just gives...

I was trying to Go from the uncertainty principle to its energy-time counter part. i know the maths is a bit off,but the idea is correct? dx=position p=momentum e=energy \upsilon=frequency \lambda=wavelength c=velocity of electromagnetic radiations dt=time now , \lambda=h/p....(i)...

hi pf, i am so confused with this energy time uncertainty principle. Somewhere i find that this means law of conservation of energy can be violated for a while and somewhere i find this still being a mystery? please help me out.

Homework Statement A Na atom is in an excited state for a mean time of 1.6 \times 10^{-8}s. Then it jumps to the ground state emitting a photon with 2.105 eV of energy. Find the energy uncertainty of that excited state. Homework Equations The Attempt at a Solution I don't even...

Hi, Consider a laser source of frequency f. This source is projected to a target at a distance D, so that the light needs time T = D/C to reach the target. I will consider the particle behavior of light in this situation. I will study the motion of one of the photons. At the exact time T/2...

Doubts about wave particle duality I know that a wave packet is formed by superposition of several individual waves having different wavelength.And the resultant wave has varying amplitudes.And from these amplitudes we can find the likeliness of the object to be in that position. My doubt is...

Hello! I am using physical data to do an analysis (~30k measurements). These measurements include energies, momenta, angles... of particles. I am calculating a value (call it v) at the end after a lengthy process, and if I introduce all the data into my program I did, the result is v±σ...

could we able to measure the velocity for a free particle with uncertainty equal to zero, could we able to have a certain values for its velocity, and let the uncertainty of the position to be infinity is there any theoretical restrictions on having a certain value for the velocity? is there...

Homework Statement In the case of an electron wave packet, the function A(k) has a rectangular shape, i.e. it is equal to A0 if k0-a<k<k0+a, and zero everywhere else. (a) Find the minimal uncertainty of electron position. (b) Find the electron wavefunction. Homework Equations ΔxΔp=h/4pi...

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

Homework Statement A pi zero meson is an unstable particle produced in high energy particle collisions. It has a mass-energy equivalent of about 135MeV, and it exists for an average life-time of only 8.7x10^-17 seconds before decaying into two gamma rays. Using the uncertainty principle...

Homework Statement The problem and its solution are attached as TheProblemAndSolution.jpg. Homework Equations Δx = λ/sinθ Δp_x = 2h/λ sinθ The Attempt at a Solution In the equation given in the problem (Δx = λ/sinθ), why is the uncertainty of the ELECTRON written as a function of the...

Does anyone know how to calculate absolute uncertainty?? A student repeatedly measures the time taken by an object to cover a certain distance and obtains the following data: t1 = 2.432 s, t2 = 2.393 s, t3 = 2.402 s, t4 = 2.412 s, t5 = 2.424 s The instrument uncertainty is 0.001 s What...

Homework Statement I conducted an experiment which involves measuring two distances (Y and L) and have used tan to determine the angle, then finally calculated the sine of the angles for use in my analysis. I have uncertainties in both length measurements and am unsure how to propagate the...

Homework Statement I was looking at a solution inmy notes which begins: ΔE = hc/λ -1st eqn ΔEΔt ~ (h-bar)/E -2nd eqn Δt ~ (h-bar)/ (hc/λ) Δt ~ λ/2∏c (where 'c' is the speed of light) What formula has been used to go from: Δt ~ (h-bar)/ (hc/λ) to Δt ~ λ/2∏c...

Another question I have concerns a table's surface area. If L=122.14±0.14[cm] and W=24.30±0.57[cm], I got that S=2968.00±69.70[〖cm〗^2], using ∆S=√((∂S/∂L)^2 〖∆L〗^2+(∂S/∂W)^2 〖∆W〗^2 ). Would you kindly confirm this result? Is it plausible that ∆S would be nearly 70 cm^2??

What is the Heisenberg Uncertainty Principle Formula? Here: http://www.people.vcu.edu/~rgowdy/mod/122/xmp4.htm It is quoted as Δx(Δmv) ~ h/2∏ which is ΔxΔp ~ (h-bar) Here: https://en.wikipedia.org/wiki/Uncertainty_principle It is quoted as ΔxΔp ~ (h-bar)/2