Uncertainty Definition and 1000 Threads

Homework Statement Calculate [x,px] = (xpx - pxx) Do this for a function f(x). Now calculate [x,py] for f(x,y) Homework Equations px is actually px hat, I'm just not familiar with latex code. px= -i (d/dx) The Attempt at a Solution I believe I got the first part, for...

Homework Statement The uncertainty ΔB in some observable B is given by a formula ΔB = √<B^2> - <B>^2. Use this formula to determine the uncertainty in position, Δx, and momentum Δp, for the ground state of a quantum-mechanical particle of mass m is a 1-D 'box' of length a, and show that the...

YBa2Cu3O(7−x)(s) + ([ 7/2]−x)H2(g) → [ 1/2]Y2O3(s) + 2BaO(s) +3Cu(s) + ([ 7/2]−x)H2O(g) 35.937 ± 0.005 mg of solid YBa2Cu3O(7−x) reacts completely, according to the above equation, in a stream of hydrogen gas at 1000°C, leaving 33.242 ± 0.005 mg of solid residue. (For the purpose of this...

Homework Statement A particle of mass m is subjected to a potential V(x)=Kx.Use uncertainty principle in the form Δx.Δp≈h(bar)/2 to estimate ground state energy of the particle. The Attempt at a Solution I have no idea. :(

Homework Statement M = (a-b)/2 + a a = 15 b=5 What is the uncertainty in M if the uncertainty in a and b is ±0.7? Homework Equations for c = a + b Error in c =√[(error in a)^2 + (error in b)^2] The Attempt at a Solution Error in M = √[0.7^2 * 3] = 1.2124 The problem...

Homework Statement What is the uncertainty in x and p of the coherent state |z> = e^{-|z|^2/2} \sum\frac{z^{n}}{\sqrt{n!}} |n> Homework Equations ... The Attempt at a Solution This seems pretty straight-forward to me. You just find the expected value of (let's say) x...

If I have the uncertainty in R and I want the uncertainty in ln(R). Am I right in thinking the uncertainty in ln(R) = (uncert in R)/R? Thanks

Homework Statement An excited atomic state has a lifetime of 1 ms. What is the uncertainty in its energy? The photon emitted during its decay is 550 nm in wavelength. What is the uncertainty and fractional uncertainty in its wavelength? Homework Equations ΔEΔt≥hbar/2 The...

Hi, I've just got a question about uncertainties that came up while doing a lab report. I have a set of data for currents required to cancel the deflection of an electron beam caused by the Earth's magnetic field: 0.195 A 0.220 A 0.250 A 0.251 A 0.239 A Because of the difficulty in...

If an atom transitions from an initially excited state emitting a photon E=hf and going to the ground state, and since ΔxΔk=1 show that ΔEΔt = hbar. So I know Ephoton=hf=hbar*sqrt(k/m) = hbar * sqrt(1/Δx*m) and since E=pc and p=hbar*k=hbar/Δx but I am not sure what to do from here? Any...

Hi all, as a complete noob, I must first ask that people understand that I have only a layman's understanding of cosmology. However, after watching a few of Brian Cox's lectures on entropy and the heat death of the universe, I had a rather interesting thought (although as I am not a...

Hi, I have formulated what I believe to be a generalized(to some degree) optimization under uncertainty problem. The write up is included in the attached file. I would appreciate any and all input, help or guidance as to how this problem could be solved. If you have any questions please feel...

Simple average question using sig figs within ± 0.0 ? Homework Statement Consider the following measurements of mileages: 23.8 mph, 20.1 mph, 26.5 mph, 20.7 mph, 21.7 mph, 27.6 mph, 30 mph, 28 mph, 27.4 mph, 34.3 mph, 26.5 mph, 32.7 mph. What is the average mileage (using...

I am stuck on one part of my Quantum Mechanics HW. Above the question it says "Try and answer the following question." So I can only assume that he isn't looking for something incredibly detailed. (Ill explain why after the question is given.) Homework Statement What is the meaning of the...

Homework Statement A useful kinematic equation is (vf)^2 = (vi)^2 + 2ad You drop a ball (with zero initial velocity) from the top of a building to measure the acceleration due to gravity. If you measure the final velocity to be vf ± ∆vf, and the height of the building to be d ± ∆d...

Homework Statement You would calculate the average velocity of the ball bearing in the fluid as v = h/t How would you calculate the absolute uncertainty on v? a) h(Δh/t) + (Δt/t2) b) (Δh/t) + h(Δt/t2) c) (Δh/h) + (Δt/t) d) h(Δh/t) - (Δt/t2) e) t(Δh/h) + h(Δt/t) Homework...

Homework Statement Calculating focal lengths of lenses. s = 144.7 ± 5.52 mm s' = 86.0 + 0.71 mm Homework EquationsFocal Length f = (s)(s') / ( s + s' ) Adding/Subtracting two numbers with uncertainties A + B ± root [ (±A)^2 + (±B)^2 ] Multiplying/Dividing AB ± root [ (±A/A)^2 + (±B/B)^2)...

Two quick problems, not sure whether the 2 are related or not: 1) The question is: A sodium atom in one of the states laveled 'lowest excited lvels' remains in that state, on average, for 1.6 x 10^-8 s before it makes a transition to the ground level, emitting a photon with wavelength...

A huge common misconception about brain function is that function can be localized to "very" specific locations. However, reductionism falls apart when speaking about emergent phenomenon such as higher order brain functions (e.g. feeling of knowing, consciousness, visio-spatial processing). Just...

I want to calculate the uncertainty in the period for a spring, when I have measured the extension of it under the influence of gravity. Call that x and say I got: x=0.10m ± 0.01 And we know that: T = 2∏√(x/g) Is it then correct to use the following formula for the uncertainty σT: σT =...

hi my concern is, that there is a huge amount of equations that are somehow related to the uncertainty principle and it is not straightforwardly obvious to me, when i have to use which of them. let me put it this way: as far as i see, there is this overall applicable equation that says ΔxΔp ≥...

Hi, I have some experimental data as a function of time t and temperature T. I have done a least squares fit of the data with a function f=f(a1,a2,t,T) (the function is non linear in a1 and a2!). Optimization of e^2 = sum((yi-f(a1,a2,ti,Ti)^2) with Matlab's fminsearch gave me a1, a2 and the...

If I understand correctly, the uncertainty principle works, because in order to measure the position accurately, you need a smaller wavelength. But observing with a particle with smaller wavelength means observing with a particle with larger momentum. Therefore, when the observation is made by...

I used a sound sensor in my experiment and hooked it up to the computer and used it to plot a graph of amplitude against time. I then too readings straight off the graph. How would I go by giving a value for the uncertainty in the amplitude?

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 completely understand the uncertainty principle and why we can't pinpoint the exact location of an electron. but what if we could?? would it be important that would could find the location of an electrom? would we know more about atoms?

Is there a mathematical or physical proof for uncertainty principle other than the one that says if you want to observe a particle you should collide with it,a photon and blah blah blah ? I can't accept that as a proof.Because It falls if you find another way of measuring the position of the...

Suppose I have an electron gun that shoots electron with momentum p (no uncertainty) at t=0, then at t=t0 I can calculate the exact location of my electron, with no uncertainty. Violation of uncertainty principle?

Homework Statement I am doing this calculation in my lab: h = sin(24.0°)[(180.0cm)(1m/100cm)] The uncertainty on the angle is ±0.5° and on the length it is also ±0.5cm. How can I go about calculating the uncertainty? If you know the answer, do you mind putting it in terms of a...

[FONT="Courier New"] [SIZE="3"] To my understanding Heisenberg Uncertainty Principle, states that we do not exist due to the fact that atoms("what we are made of") are not present, when they are not consciously observed. Please elaborate.

Homework Statement A student makes measurements from which she calculates the speed of sound as 327.66ms–1. She estimates that her result is accurate to ±3 %. Which of the following gives her result expressed to the appropriate number of significant figures? A 327.7ms–1 B 328ms–1 C 330ms–1 D...

I started this thread to continue a conversation from another thread. Does HUP imply randomness? What really is the definition of randomness? I would say that HUP does not imply randomness, but just tells you the relationship between how the state vector is spread out along the basis of two...

Homework Statement So basically I have plotted two variables I measured on a graph, which gives a simple linear relationship, and have found the gradient and standard error of the gradient (1.21251 and 0.03275 respectively). Now my problem is that this gradient is equal to a constant divided...

hi this is my first physical post , i hope i find the right help i just want to know the meaning of uncertainty and the difference between unceratinty and errors any explanation would help

Hi, first of all, sorry if my English is not perfect I'm from Quebec City and English is not my first language. I'm trying to make a scatter plot with average of numerical data. But now I also want to put the standard deviation on the scatter. Exemple, I have a point (x,[y ± σ]) and I...

I am trying to figure out how to refer to two overlapping uncertainty results. I have to write a conclusion and I find it difficult to explain. Even now it may seem unclear as to what I am referring to so I will provide an example. This is directly from my conclusion. 'The 72 rated golf ball...

I am trying to figure out how to refer to two overlapping uncertainty results. I have to write a conclusion and I find it difficult to explain. Even now it may seem unclear as to what I am referring to so I will provide an example. This is directly from my conclusion. 'The 72 rated golf ball...

I'm a bit confused about how the uncertainty principle allows for the spontaneous creation and annihilation of virtual particle pairs. I can understand that energy conservation can be violated for a very short time as per delta_e*delta_t > h_bar/2. However, when the virtual particle pair...

Homework Statement In Bohr model of the hydrogen atom, the max. kinetic energy that an electron can have is around 13.6 eV, as it would otherwise not be confined to the atom. Uncertainty Principle: ΔxΔy ≥ h/2π a) Find the max. momentum of such confined electron. b) Use Uncertainty Principle...

it should be called as unpredictability rather than uncertainty principle because the event is certain but we cannot predict it.

how Energy time uncertainty principle account for the broadening of a level? thanks in advance

Homework Statement Determine the energy uncertainty \Delta E = \sqrt{<E^2> - <E>^2} for a particle described by a wave function \Psi (x) = c_1 \psi (x)_1 + c_2 \psi (x)_2 where \psi_1 and \psi_2 are different (orthonormal) energy eigenstates with eigenvalues E_1 and E_2. Homework...

hi i am looking for the correct equation, that gives me the linewidth by knowing the time of the emission process. so far, i found in the internet: Δf=1/(Δt), Δf=1/(4πΔt) and Δf=1/(2Δt) can you tell me, when i have to use which of these equations and maybe whether you think that...

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 Show that, if [H,A] = 0 and dA/dt = 0, then <&Delta;A> is constant in time. Homework Equations d<A>/dt = <i/ℏ[H,A] + dA/dt> The Attempt at a Solution I am trying to use the above equation to show that d<&Delta;A>/dt is 0, and I can get to d&Delta;A/dt = 0, but I...

Homework Statement The linewidth of a certain fluorescing dye molecule is 60nm and the peak emission wavelength is 600nm. The lifetime of the dye molecule in the excited state is 1ns. Determine whether the linewidth of the emission is a result of the uncertainty principle. (it may be helpful...

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...

Homework Statement Use the uncertainty principle to estimate the ground state energy of a particle of mass "m" is moving in a linear potential given by V(x) = ∞ for x≤ 0 V(x) = αx for x ≥ 0 Homework Equations ΔxΔp ≥ h/2 The Attempt at a Solution I've looked at a similar problem...

What's the kinetic energy uncertainty for gaussian wave packet ψ(x)=((α/pi)^(1/4))exp(-αx^2/2)?

Homework Statement I am having trouble calculating uncertainty when a number is added to a value with uncertainty. M = 350g a = 0.624 \pm 0.001 µk = 0.07 g = 9.80 m/s2 Homework Equations T = M*a + µk*M*g The Attempt at a Solution T = (350g)*(0.624 m/s2) +...