Questions tagged [heisenberg-uncertainty-principle]

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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What is the relationship between the Heisenberg uncertainty principle and the principle of complementarity?

My textbook appears to imply that the principle of complementarity is a consequence of the uncertainty principle: The uncertainty principle allows us to understand why it is possible for radiation, ...
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Is quantum uncertainty of particle location bound by the speed of light?

If I measure the location of a quantum particle and then measure its location 1 second later, is there a probability larger than zero that I find it in a location farther away from the first location ...
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Confusion over the meaning of the Uncertainty Principle (practical limitation vs precise measurement being meaningless)

So far, I have seen two meanings of the Heisenberg Uncertainty principle through two derivations. One interpretation is that the observation of a particle requires the interaction of an electron which ...
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ER = EPR and Heisenberg uncertainty principle

Following the Maldacena-Susskind "ER = EPR" correspondence, what gravitational fact would the Heisenberg uncertainty principle correspond to?
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Derivation Heisenberg Uncertainty

I know there have been many questions posted regarding the derivation of the Heisenberg Uncertainty. I do not want to derive its general form, but instead I would like to calculate its lower minimum ...
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What is the meaning of uncertainty principle in the case of hidden-variable theories?

What would be the meaning of the uncertainty principle in the case of hidden-variable interpretations of quantum mechanics, especially contextual hidden-variable theories? Edit: Another way to put ...
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The Mathematic Tricks in the Derivation of Heisenberg Uncertainty Principle

I'm studying the derivation of Heisenberg Uncertainty principle but stuck with the mathematic trick. When deriving Heisenberg Uncertainty principle, consider a function γ(t): $γ(k,t)\equiv([t−(t)]−iκ[...
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In the double slit experiment, when a particle is bombarded between two slits, why doesn't it "always" hit between the two slits and not pass at all? [duplicate]

The alignment is always towards the centre of the area between two slits.
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Explanation of spontaneous emission using uncertainity principle

How to understand spontaneous emission using Heisenberg's uncertainity principle? Why does it occur?
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Relation between the lifetime of gain medium and laser frequency bandwidth in $\rm HeNe$ laser

When I am studying about Spiking phenomenon of lasers, I found this "spiking occurs for lasers where the upper-state lifetime is much larger than the cavity damping time. Gas lasers often ...
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Derive Heisenberg Uncertainty from General Uncertainty Principle

The General Uncertainty Principle of 2 Operators is given by $$(\Delta X)^2\,(\Delta Y)^2 \geq\left(\dfrac{1}{2}\big\langle\{X,Y\}\big\rangle - \big\langle X\big\rangle \big\langle Y\big\rangle\right)^...
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Fourier Transform of a Wave Function relating to Position and Momentum

Why is it that, in quantum mechanics, the fourier transform of a wavefunction of the position of a particle is the wavefunction of it's momentum? I'm trying to learn about the uncertainty principle, ...
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Proving the uncertainty relation for the quantum covariance matrix

In quantum optics papers we often encounter this version of the Heisenberg uncertainly relation (for an $n$-mode quantum system): $\sigma + \iota \Omega \ge 0$ Where $\sigma$ is the covariance matrix $...
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Wrong formulation of Heisenberg's uncertainty principle [closed]

My professor wrote this on the blackboard: $$\Delta E\Delta t \leq \hbar$$ Isn't the $\leq$ sign wrong? Or is this "another" possible formulation of Heisenberg's uncertainty principle? I am ...
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Relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread

Consider a wave packet that satisfies the relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread appreciably in the time it ...
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Is there consensus among physicists that reality is fundamentally deterministic? [duplicate]

Does Heisenberg’s Uncertainty Principle mean that the universe cannot deterministically be predicted by observers, or does it mean that the universe is inherently indeterministic, meaning that the ...
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In quantum experiments are we measuring the quantum state of a system or are we measuring the effect of the measurement on the quantum state?

At the macro classical world, measurements in experiments when done correctly interfere very little with the state of the system under investigation. As an example a digital ohmmeter with very high ...
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Uncertainty principle when the expectation value of commutator is zero

I'm reading section 4.3 of Introduction to quantum mechanics written by David Griffits. The book states that the product of the standard deviation of two components of angular momentum is greater than ...
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Is this Fourier derivation of Heisenberg principle true?

I noticed that I can derive Heisenberg principle very easy. $\begin{aligned}p=\dfrac{h}{\lambda }=\dfrac{h\nu }{\lambda \nu }=\dfrac{h\nu }{c}=h\nu \left( c=1\right) \\ Fourier\Delta v\cdot \Delta x &...
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Definition of a wave packet

In Shankar's QM book page 168, the author stated a wave packet is any wave function with reasonably well-defined position and momentum. What does he mean by resonably well-defined position and ...
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Uncertainty of waves

Here in the pictures I have written about some question I have been thinking about a long time, what do you think? Link to the chapter I am talking about: http://www.its.caltech.edu/~matilde/...
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Since surface tension and area are conjugate variables, is there a uncertainty relation between them? $\Delta \gamma \Delta A \geq \text{constant}$

Since all conjugate variables have uncertainty relations like ; $$ \Delta f \Delta t \geq \text{constant}$$ $$ \Delta \lambda \Delta x \geq \text{constant}$$ Etcetera, is there also a 'uncertainty ...
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The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?

I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
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Taking into account the Pauli Exclusion Principle, how many particles can you cram into a really small space?

I'm trying to understand the basic concept of the Pauli Exclusion Principle, but my former question here did not provide an answer. So let me rephrase it. One way of describing the PEP is that you ...
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Why do we keep referring to the Heisenberg Uncertainty Principle in situations that we don't - and can't - know about? [closed]

In all of my reading in physics, I have been surprised by the number of times that I read "this can't exist" or "that can't exist" because of the Heisenberg Uncertainty Principle. ...
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Is there a minimum value different from zero for the uncertainty in momentum for a particle in a box?

Lately, I have been studying QM more deeply and I just discovered how many important subtleties the 'well-known' particle in an infinite potential well hides, which are precious for extending ...
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Heisenberg microscope for momentum

In the "Heisenberg microscope", the position of a particle is measured using a photon. The higher the photon energy, the better the precision in measuring the particle location is, but the ...
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How is the Heisenberg Uncertainty calculated value added to a measurement error bar?

It is not clear to me if the calculated HU for a specific experiment is added to the measured value Gaussian curve together with the statistical errors (i.e. added to the total error bar) of this ...
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Common eigenstate of incompatible observables

In many resources I have seen that incompatible observables cannot have a common eigenbasis set, but may share one or few eigen states. I followed the thread Can incompatible observables share an ...
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How is spooky action at a distance measured?

My recent background reading: https://www.science.org/content/article/more-evidence-support-quantum-theory-s-spooky-action-distance I have been trying to understand how experiments actually measure ...
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What is the value of Heisenberg Uncertainty in position $Δχ$ for a free electron at rest? [duplicate]

Any analytical calculation of this value included in a canonical answer would be nice! We know according to HUP that: $$ \Delta x \Delta p \geq \frac{h}{4 \pi} $$ $\Delta x=$ uncertainty in position $\...
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What happens to the wavefunction of an electron trapped inside a nonreflective sensor-container? Does it prove HUP is only an epistemological limit? [closed]

Assume there is a spherical container of diameter of 1m, inside which at the center of which an electron is introduced at near zero velocity as limited by Heisenberg Uncertainty Principle(HUP) say at ...
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In the case of a free wave function, does $|p| = E_k = 0 \mapsto |v|=0$?

This answer indicates that "it is not possible to talk about a particle 'stopping' or being 'stopped' in any meaningful or non-contrived sense" because of the Heisenberg indeterminacy ...
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Number-Phase uncertainty relation

I was trying to understand the Number-Phase uncertainty mainly following "A. Duncan, The Conceptual Framework of QFT", pages 223-233 and I got stuck into the definition of the operator $$E = ...
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How would you prove Heisenberg's Uncertainty Principle without making use of fancy language? [duplicate]

The title speaks for itself. What would be the down-to-earth meaning behind this principle beyond the incomprehensible mathematics and the abracadabrant lingo? (such as the wavefunction suddenly ...
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In uncertainty principle of waves

In uncertainty relations between freq. and time, if you had a part of a wave but not the entire cycle,(thus it is said that the frequency/wavelength is uncertain) couldn’t you based on the short curve ...
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Conceptually understanding an Ising-type transition

I am currently reading the following paper. The system consists of a chain of mesoscopic superconducting islands (aka a Josephson Junction array), but each island also contains a quantum wire that ...
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Uncertainty principle in deformation quantization

Deformation quantization procedure is a well-known way to quantize a classical phase space (at least formally for Poisson manifolds which is known as formal deformation quantization). Although it is a ...
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What is the theoretical limit on accuracy of an idealized photon detector?

I know that Heisenberg's Uncertainty Principle and the Observer Effect mean there is a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of particles (...
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Uncertainty Principle in 3 dimensions

I'm trying to understand how to write Heisenberg uncertainty principle in 3 dimensions. What I mean by that is to prove something of the form $f(\Delta p_x,\Delta p_y,\Delta p_z,\Delta x,\Delta y,\...
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What is the meaning of an object having an uncertainty of velocity of 2 $\rm m/s$?

In several questions we are given the uncertainty in velocity of an object and are asked to calculate the uncertainty in position of an object? Well my doubt is that,as when we say that the ...
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Can a single photon have exact energy or momentum? [duplicate]

From the Wikipedia page on single photon sources: ...
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Robertson uncertainty relation for the angular momentum components

I'm studying orbital angular momentum in the quantum domain, and I've arrived at the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is ...
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How does the Fourier picture relate to non-commutativity?

A compelling video by 3Blue1Brown visualizes the uncertainty principle with Fourier transforms. The gap I'm trying to bridge is between this "Fourier picture" and the matrix-based statement $...
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Uncertainty principle manifesting in $j(j+1)$ vs $j^2$

To motivate my question, please consider a system with total angular momentum $j$. The fact that the largest eigenvalue of $J_z$ is $j$, while $J^2 = J_x^2 + J_y^2 + J_z^2$ has all eigenvalues equal ...
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Repeating observations in quantum theory

Suppose we prepare a state $\psi$ in a quantum system, represented in some Hilbert space, and suppose $A$ is an observable represented by the matrix $A$ (which possibly has infinite order). QUESTION A ...
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Is the uncertainity principle explained by disturbances or only by the Fourier picture?

Qualitatively, the tradeoff in uncertainty between two non-commuting observables $\hat{x}$ and $\hat{y}$, could be explained by... the Fourier picture where the more one variable is defined (i.e., ...
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Does a Gaussian wavepacket disperse with time or not? [duplicate]

There are many questions on this site relating to the spreading of Gaussian wave packets and the time dependence of the uncertainty in position ($\Delta x$). For example, see Is it possible for $\...
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Narrow-bandwidth laser and its beam size on uncertainty principle

I read that a single frequency laser can have a bandwidth as low as a few kHz, but according to the uncertainty principle, $\Delta x \Delta p = \Delta x \Delta f h/c >=\hbar $, so $\Delta x \sim ...
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Why exactly can we not know the position and momentum of a given particle?

I have heard that this is to do with the fact that a particle is also a wave. However, I do not understand why this would cause this. Surely, you could use the formula used for finding the velocity, ...
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