This tag is for Heisenberg's quantum mechanical uncertainty principle. DO NOT USE THIS TAG for uncertainty in a non-quantum measurement.

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Is there scattering event if two wave functions overlap in momentum space?

Let's consider two particles, moving, for simplicity, in a 2D plane, represented by their wavefunctions in the form of (when being modulus squared) very very very narrow Gaussians (let's say close to ...
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Key Assumption to derive the Uncertainty Principle — Canonical Conjugate Operators [on hold]

From this related question, Rigorous Mathematical Proof of the Uncertainty Principle from First Principles The key assumption to derive the uncertainty principle seems to be the relationship ...
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How to use Heisenberg to explain atom cannot be at rest

In a Dutch national physics exam at the level just before entering university there was a question about a molecule HI: one atom hydrogen plus one atom iodine. Within the molecule, the hydrogen ...
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'The size of an atom' using Uncertainty Principle

Suppose we have a hydrogen atom, and measure the position of the electron; we must not be able to predict exactly where the electron will be, or the momentum spread will then turn out to be infinite. ...
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Rigorous Mathematical Proof of the Uncertainty Principle from First Principles [duplicate]

While looking at an intuitive explanation for the Heisenberg Uncertainty Principle (related question below), there was a mention of an axiomatic approach to establishing the uncertainty principle. ...
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Why can the y and z-components of spin be measured simultaneously? [duplicate]

I have a gut feeling that this is wrong. By the uncertainty principle where $x,y,z$ are the $x,y,z$ components of spin $$ \sigma_{y}\sigma_{z}\geq \frac{\hbar}{2}\langle x \rangle $$ and it can be ...
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Why only 1 component of angular momentum?

Griffiths says that you can have only 1 well defined component of the angular momentum because of the uncertainty principle. From the uncertainty principle, we get that $$ \sigma_{L_x}\sigma_{L_y} \...
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Is the single slit experiment a practical example of Heisenberg's uncertainty principle?

I saw some videos where a person points a laser through a slit. As they reduce the width of the slit, the diffracted image spreads out, like this: Can this pattern be viewed as a consequence of ...
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Doesn't quantum uncertainty disprove string theory? [duplicate]

String theory states that the oscillations of little strings are responsible for all the particles in and the evolution of the universe. The specific type of particle created by a string depends on ...
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203 views

Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq |\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\langle \...
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Why is the Heisenberg uncertainty priciple considered as a universal truth? [duplicate]

You should have heard about Heisenberg and his uncertainty principle. I want to know why it is considered as a universal truth, and not a technological limitation. I'd prefer an elaborate answer with ...
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Calculating Natural Broadening of Emission Lines

I'm trying to demonstrate the small effect of Natural Broadening as compared to other types of broadening (Doppler, Stark, van der Waals, etc.) and my calculations don't match the accepted values. My ...
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Why does $\Delta x \Delta p_x$ increase linearly with $n$ for stationary states?

Harmonic Oscillator $\displaystyle \Delta x\Delta p_x = \hbar \left(n+\frac{1}{2}\right)$ Particle in a box $\displaystyle \Delta x\Delta p_x = \frac{\hbar}{2} \sqrt{\frac{n^2\pi^2}{3}-2}$ ...
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1answer
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Modern interpretation of wave-particle duality

As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and particle-...
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Why doesn't position and momentum commute? [duplicate]

I'm trying to understand the reason for Heisenberg's uncertainty principle which I read is a "fact of nature" rather than an experimental limitation. I found this thread in which the accepted answer ...
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No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
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Uncertainty principle-Exact Measurement of one observable possible?

I'm currently learning for my exam in physical chemistry and have the following question: According to the uncertainty principle the momentum and the location cannot be measured exactly at the same ...
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How do I get observables to calculate uncertainty?

Given an infinite potential square well with $0<x<L$, I need to calculate the uncertainties of position and momentum. The eigenstates in the position basis are $$\lvert E_n\rangle\to \psi_n(x)=\...
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Heisenberg uncertainty principle

In the double slit experiment, an electron interferes with itself and creates the pattern because it is in a superposition, traveling through both slits. If we place a detector at one slit, the wave ...
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Heisenberg's uncertainty principle for mean deviation?

The Heisenberg uncertainty principle states that $$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$ However, this is only for the standard deviation. What is the inequality if the mean deviation, defined as ...
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1answer
269 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
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Why doesn't this experiment violate the Uncertainity Principle?

Is it possible to slow an electron in such a way(for example using a cyclotron to decelerate the electron ) that it completely stops. And since we created the slowing mechanism we might be able to ...
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How does the uncertainty product $\Delta x \Delta p$ behave for the bound states of the triangular potential?

As has been remarked earlier, if you take an unbounded potential $V(x)$ (so that all the eigenstates are bound) and you look at the uncertainty product $\Delta x\Delta p$ as a function of the index $n$...
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Conservation of Energy and Quantum Fluctuations

Regarding conservation of mass-energy Wikipedia says: "this is an exact law, or more precisely, has never been shown to be violated." However, regarding quantum fluctuations, Wikipedia says here: "...
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Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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How do we determine the location of particles? [closed]

Can someone explain how the location of a particle is determined both theoretically and experimentally (if possible)? Can the location of a particle be given by the uncertainty principle? (dividing ...
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Uncertainty and Classical waves

My professor, introducing Heisenberg uncertainty principle, started from the Fourier transform and the classical uncertainty for waves. He told about the localized impulsive wave $\delta(x)$ which ...
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Uncertainty Relations, Conjugate Quantities, and Fourier Transforms

I've heard from a lot of people that the reason momentum and position have an uncertainty relation is because of the Fourier Transform. But is this in any way the case? If it were I would expect all ...
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Uncertainty principle-QM [duplicate]

I some trouble understanding the uncertainty principle. I understand most of the math derivation but not the physics. Is there any intuitive explanation of this idea, and why is the uncertanty does ...
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A question about heisenberg uncertainity principle

In my textbook about atomic structure we have a brief part about Heisenberg uncertainty principle. While the derivation was not given in the book which simply stated Heisenberg as $\Delta x\, \Delta p\...
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Isn't the uncertainty principle just non-fundamental limitations in our current technology that could be removed in a more advanced civilization?

From what I understand, the uncertainty principle states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on ...
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Is there something behind non-commuting observables?

Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no ...
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Is this statement of the Heisenberg uncertainty principle correct? [duplicate]

Is this correct? The Heisenberg Uncertainty Principle is not a Principle or law of physics. It's one of many results you can work out from quantum theory with some math: -- In quantum theory ...
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Is there an actual proof for the energy-time Uncertainty Principle?

As I understand, the energy-time uncertainty principle can't be derived from the generalized uncertainty relation. This is because time is a dynamical variable and not an observable in the same sense ...
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Uncertainty principle explanation

Just finished reading "In Search of Schrödinger's Cat". I am currently trying to explain the Uncertainty principle to myself as if I was 5. Concretely, why it is not possible to measure both position ...
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Heisenberg uncertainity principle is valid in the case of QFT? [duplicate]

The Heisenberg uncertainty principle is valid (or taken into account) in the case of QFT?
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Is there any uncertainty between mass and proper length or time?

I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
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Confusion regarding Vacuum fluctuations, Strings & The Casimir Effect

From Wikipedia: Casimir Effect The typical example is of the two uncharged conductive plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field ...
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Heisenberg's uncertainty principle for electrons and atoms

Here is a video of Michio Kaku discussing Moore's Law and the quantum mechanical limits thereof. Around the 1:30 mark he's talking about how the chips today have a layer of 20 atoms across (I'm ...
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Is it possible for $\Delta x$ ($\sigma_x$) of any free particle wave packet to be decreasing at any time?

Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens ...
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Does Heisenberg's uncertainty under time evolution always grow?

Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting ...
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Are there any practical applications of the uncertainty principle

I believe GPS works because of extremely small time differences between the satellites. Because of how small the time differences are, it needs to take into account gravity's effect on time. ...
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Proof for fluctuations in vacuum

I'm not a physicist. My understanding of Heisenberg's uncertainty principle and its proof (that is given by an imaginary microscope) is that for example: at a specified time determining the exact ...
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1answer
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Does Heisenberg's uncertainty hold for any two quantum measurements?

Heisenberg's uncertainty principle is most commonly expressed in terms of the uncertainty in measurement of position and momentum of a particle, $$\Delta x\Delta p \geq \hbar$$and uncertainty in ...
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What is meant by “Nothing” in Physics/Quantum Physics?

I am not a phycisist, so please forgive my ignorance. This is related to my posts and this. I am trying to understand what is meant by the term "Nothing" in physics or Quantum Field Theory (QFT) since ...
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Uncertainty Principle with the corresponding operators

Why does the corresponding operator do not commute if there is uncertainty related to two observables A and B that states $\Delta A\,\Delta B > 0 $ ?
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Measurements in quantum mechanics

Why does measurement change things? I read that measurement changes things because we have to bounce photons off an object to 'see' it and that changes its position, momentum etc... But on the other ...
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1answer
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What is the accuracy when firing an electron at a target?

Consider firing an electron at a target. Let the target be at a distance $d$ and the electron be travelling at a non-relativistic speed $v$. How can we estimate the maximum possible accuracy ...
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Uncertainty principle and digital camera

I recently got into a discussion in how far (miniaturized) digital cameras are affected by the uncertainty principle. Specifically the question was, whether the uncertainty principle is one of the ...
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Heisenberg's uncertainty principle derivation in a ring [duplicate]

The standard derivation But now suppose the space is a ring of length $L$, it seems the derivation could work out exactly the same and we get $$\Delta p \Delta x \geq \hbar/2.$$ But since $\Delta x$ ...