Uncertainty Definition and 1000 Threads

I KNOW this is going to be a very basic question for most of you but I am new to PF which seems awesome by the way and generally new too physics too. My question that my teacher went over on the practice questions for home was determine the percent uncertainty of the number 1.56. I know...

Uncertainty partial derivatives Homework Statement 1 a) Give expressions for the uncertainty in both the area and volume of a right circular cone with radius R and height H and side length S. Assume that the radius has uncertainty σR and the height has an uncertainty σH. <----First part...

A position of a particle in linear motion is given by: x = vt + 0.5at2 Calculate x with the error for: t = 25.3 ± 0.5s v = 10.1 ± 0.4m/s a = 2.5 ± 0.3m/s2 So for calculating vt: q = (10.1) (25.3) = 255.53 (exact) Δq = (10.1)(25.3) * √ (0.4/10.1)2 (0.5/25.3)2 = 11.31... Therefore, vt =...

Homework Statement As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 ± 0.02 cm and a thickness of 0.050 ± 0.005 cm. (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio...

Homework Statement What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r=5.60±0.05m? Homework Equations ∏r^2 The Attempt at a Solution

Homework Statement Approximate uncertainty in the area of a circle of radius 5.5×10^4 cm? Homework Equations πr^2 The Attempt at a Solution

"5 students time a bowling ball traveling from point A to point B. They record the following times": 2.45s 2.49s 2.58s 2.55s 2.51s "7 students measure the length of a car. They record the following lengths": 4.5 m , 4.7 m , 4.4 m , 4.6 m , 4.8 m , 4.5 m , 4.6 m Homework Equations...

I read somewhere that Heisenberg described his uncertainty principle by saying that you can't measure position more accurately than the wavelength of light (which makes sense), so Δx > λ. This is what I don't get. He then says that p=h/λ, so Δp > h/λ2 Δλ. He the multiplies and sets Δλ ≈ λ to...

Homework Statement A spin-half particle is in a known eigenstate of Sz. Show that the product <S^2_x> < S^2_y> is consistent with the Uncertainty principle Homework Equations The Attempt at a Solution I know that the generalized uncertainty principle gives ΔS_x ΔS_y ≥ |<[S_x...

Homework Statement Hello, I have solved the problem, but not the way the writer intended. I need help figuring out how they wanted me to do it. Here's the problem: The circumference of a sphere is found to be 0.98 m +/- 0.01 m. Calculate the volume and absolute error with five digits...

I have been going through my Physics textbook to brush up on my Quantum Mechanics before starting my next QM course next academic year and the Heisenberg uncertainty principle for position and momentum is written as ΔxΔp ≥ h-bar when I thought it was ΔxΔp ≥ (h-bar)/2. Other sources say it is...

Here's my problem: I have been using a digimatic indicator tool to measure the thickness of a somewhat uneven film. The digimatic indicator has a digital screen that shows up to 1 um, but according to specifications the accuracy is only 3 um. To account for the uneveness I have taken 10...

Hi to all, I have the following problem: I want to characterize two lots of detectors in order to retrieve their mean cross section and standard deviation for a proton beam. For cross section I mean the number of counts respect the fluence of particle (fluence = integral of the particle flux...

Homework Statement The manufacturer of a digital ammeter quotes its uncertainty as ±1.5% ±2 digits. a. Determine the uncertainty in a constant reading of 2.64 A b. The meter is used to measure the current from a d.c. power supply. The current is found to fluctuate randomly between 1.58 A and...

Homework Statement Homework Equations \begin{align} \Delta p \Delta x &\geq \frac{\hbar}{2}\\ \langle p \rangle &= \sqrt{\langle p^2 \rangle - \langle p \rangle^2}\\ \langle x \rangle &= \sqrt{\langle x^2 \rangle - \langle x \rangle^2} \end{align} I allso know that a wavefunction of a...

Lets say we put an electron in a box (spherical) which has a radius ##r##. I want to know if position uncertainty ##\Delta x = r## or is it ##\Delta x = 2r##? I need to know this to corectly calculate 1st the momentum uncertainty ##\Delta p=\frac{\hbar}{2\Delta x}## and 2nd that kinetic...

This question is regarding the boson statistics and it’s relation to the uncertainty principle. Consider we have a vacuum state and we apply a field operator on it to create a particle at position x, we end up with state like \begin{array}{l} \left| \psi \right\rangle = {\psi ^\dag...

My qm textbook, aptly named "quantum mechanics", is by McIntyre, though it omits the proof for the uncertainty principle and simply states it as ∆A∆B ≥ 1/2|〈[A,B]〉|. In words, if that's unclear, this is 'the product of the rms deviations of A and B is greater than/equal to one half the absolute...

Homework Statement An object of mass m = 2.3 ± 0.1 kg is moving at a speed of v = 1.25 ± 0.03 m/s. Calculate the kinetic energy (K =(1/2)mv2) of the object. What is the uncertainty in K?Homework Equations Δz = |z| ( Δx/x + Δy/y ) - Multiplication Δz = n (xn-1) Δx - Power The Attempt at a...

why doesn't the uncertainty principle lead to small discrepancies in the spectrum of the same element in different situations? I think that since there is a whole area for the electron to jump from and to and therefore a small range of values of possible jumps for a single shell, so there...

Hey guys, I saw a joke about this in the jokes thread. So I went to see what it is exactly. But the thing is I didn't understand it fully. Could anyone please simplify and comprehend to me? Also I saw that it's only for particles. What is the importance of this theory. I hope non complicated...

Need help propagating the uncertainty of Es = Ex ×(x+xo/xs+xo) . I understand all of the rules and can do it for a formula such as vo+ at. But I am having trouble with the (A+B)(/A+C)

Need help propagating the uncertainty of Es = Ex ×(x+xo/xs+xo) . I understand all of the rules and can do it for a formula such as vo+ at. But I am having trouble with the (A+B)(/A+C).

Homework Statement The position of a 60-gram golf ball sitting on a tee is determined within +- 1μm. What is its minimum possi- ble energy? Moving at the speed corresponding to this kinetic energy, how far would the ball move in a year?Homework Equations ## K\geq\dfrac {\hbar ^{2}} {2ma^{2}}...

Suppose we have x plates of wood of thickness (0.0150 \pm 0.0002) \text{ m} and we wish to stack them into a pile of height (1.000 \pm 0.001) \text{ m}. The number of plates x required is then x = \dfrac {1.000 \pm 0.001}{0.0150 \pm 0.0002} \, . How many plates will certainly fit in the...

As a result of some precise experimental data, we now know that the mass of the quark is not naively 1/3 the mass of the proton. The most recent estimates for the mass of the quark is: Masses of the current quarks: = 2 - 8 MeV/c2 = 1.0 - 1.6 GeV/c2 = 168 - 192 GeV/c2...

Hi! I found a few old threads lying around regarding this, such as this one, but I thought I'd start a new one asking the question in my own way. So here goes. Is the uncertainty described by the Uncertainty Principal a result of the fact that by measuring something we affect it, or a...

Homework Statement In a scanning electron microscope, a 0.3 keV electron beam, collimated by an aperture of width ∆xi, is directed towards a target 1 m away from the aperture. Assuming a field-free region from aperture to target, the uncertainty ∆xf in the transverse coordinate of the...

I really can't understand the uncertainty principle,and now there are some experiment that violate the uncertianty principle, I need deepen understanding of quantum uncertainty,who can give me all the information about the uncertainty principle,such as new ideas,related study or books,thanks

Homework Statement I have to find the percentage uncertainty of a wooden block for its volume and density. Using 3 different types of measurements for length, width, and height. Let's say that this is my data (cm): Instrument 1: L= 1.1 W= 1.1 H= 1.3 V=1.573 Instrument 2: L= 1.13 W= 1.13...

Homework Statement A bumblebee is flying around your kitchen with an average speed of 5.0 m/s. You very carefully measure its position to be 3.01 m in the x direction, 0.25 m in the y direction and 1.23 m in the z direction. What is the approximate theoretical uncertainty in its...

Homework Statement Calculate the uncertainty product ΔrΔp for the 1s electron of a hydrogen-like atom with atomic number Z. (Hint: Use <p> = 0 by symmetry and deduce <p^2> from the average kinetic energy) Homework Equations All I have is the wavefunction. For a 1s, it takes the form...

This is from Hogdson's book the Mind Matters Does anyone know what the actual equation he is talking about and I was wondering if anyone could give me a few more details regarding the energy-time uncertainly relationship.

The derivation of the momentum/position Heisenberg Uncertainty Principle (HUP) is based on the statistical interpretation which says that if we have a lot of quantum systems in identical states, and measure the momentum in half of them and get a distribution with standard deviation σp, and...

If we take a narrow aperture(such as the one used in the double slit experiments) and attach a length of optical fibre to it, surely now we know the position (confined by the width of the fibre) and also the momentum(defined by the direction of the fibre). How does the uncertainty principle...

Hi everybody. I have a quick question regarding the relationship between the uncertainty principle and the measurement postulate. According to the former, the higher our certainty is about the position of a particle, the lower our certainty is regarding its momentum, and vice versa. This...

Homework Statement I'm in a Year 10 Physics class, and we have been doing an experiment about Snell's Law (θincident = θrefracted). The experimental design is fairly simple: a beam of light (from a ray box with a single slit in front of it) is shone into a glass block. The angles of the...

This may be a dumb question, but I am still new the the concept of the quantum world... If we can't measure position and momentum precisely at the same time, why can't we use 2 detectors? One to measure position, and one to measure momentum. Have them take the measurement at the same time, and...

It's .22 ± .026s I know it's wrong to have an uncertainty mor eprecise than the value, but this uncertainty was obtained through the standard deviation methos ( with the sqaure) root? What should I do?NVM I fugured it out myself.

The typical energy needed to ionise an atom is around 5 eV. Use the Uncertainty principle to estimate the size of an atom. Homework Equations E=mc^2 E = p^2/2m Δx.Δp ≥ h/4π The Attempt at a Solution So I got the mass rearranging E = mc^2 m = 5*1.6*10^-19 / (3*10^8)^2...

Homework Statement The diagram is attached. Photons are being beamed with momentum \rho_{0} and mass m at a slit of width A Estimate the uncertainty \Delta p_{y} emerging from A Sketch spot size at B as a function of slit width using the uncertainty principle Determine minimum spot size...

We have an electron pulse of width 1 nanosecond and with kinetic energy of 1keV. We have to calculate Δx and Δp. I have a question regarding this problem. If they give us the kinetic energy of the electron pulse then we know exactly the momentum right? And so the uncertainty of momentum would...

The principle states: δxδp≥h/4π I understand what it means and I've seen in proven both theoretically and expiamentally, so I am not questioning the inequality here. My question is: If there was a very narrow tube that had a vacuum inside it and a laser attached at one end that shoots...

I calulated the time(s), then i found the uncertainty as a percentage of my results. Later on i calculated 1/time and used the uncertainty % which i originally calulated. Could somebody tell me if it is relative or absoulte uncertainty and why?

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...