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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The uncertainty principle and two-particle collisions

It is not possible to simultaneously know the exact position and momentum of a particle as a consequence of non-commutativity of the position and momentum operators. But what if I consider a simple ...
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The Fisher information in QM

What is the relationship of the minimum Fisher information, Fourier transformation and position-momentum uncertainty relation in QM? To what degree these concepts revolve around the same thing?
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Different forms of Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle is often written in two forms: $$\Delta x \Delta p \geq \frac{\hbar}{2} $$ and $$\sigma_x \sigma_p \geq \frac{\hbar}{2}. $$ Are these two equivalent? I've been ...
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1answer
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Uncertainty relation in mixed states

If a system is in a pure state $|\psi\rangle\langle\psi|$ we have $$\sigma_A\sigma_B\geq\frac{1}{2}|\langle[A,B]\rangle|.$$ Generalize this and find an uncertainty relation for an arbitrary mixed ...
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How do I interpret uncertainty in velocity greater than the speed of light?

I just studied Heisenberg's uncertainty principle in school and I came up with an interesting problem. Assume an electron which is moving very slowly and we observe it with a distance uncertainty of ...
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What is the maximum number of bounces a ball can be expected to make on another fixed ball of same radius on the ground?

In the book 'Quantum Mechanics' by Leonard I. Schiff, this question can be found at the end of chapter one. More specifically it asks: A perfectly elastic ping pong ball is dropped in vacuum from a ...
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443 views

Trapping an electron

Imagine that one could theoretically trap a single electron in a small box, with walls that somehow prevent the electron from passing through and out of the box. Now, the box begins to move in on ...
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How uncertainty principle can be used to calculate the range of actual variables

I know the uncertainty relation $\Delta x \Delta p \ge \frac{\hbar}{2}$ tells the uncertainty in position and momentum, or energy and time should be greater than or equal to $\frac{\hbar}{2}$, but I ...
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Feynman's path integral and uncertainty principle?

The Feynman's path integral representation gives the quantum amplitude to go from point $x$ to point $y$ as an integral over all paths. How is that idea consistent with the uncertainty principle that ...
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Uncertainty as a founding principle of QM? [closed]

Ideally, every new physical theory is derived from its fundamental principles. Hall & Reginatto derived the Schrödinger equation from an uncertainty principle and probabilistic classical mechanics,...
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Looking for a simplified explanation for why you cannot measure velocity and pin point location

Because of uncertainty, you cannot measure both velocity and exact position. Is this because when you measure the position of a particle, it is freezing it in its frame of reference? When measuring ...
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Is it true that we can't measure position and momentum together?

The uncertainty principle states that there always will be mean variance if we measure position or momentum. It does not state that the measurement is wrong. It only states that there always will be a ...
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Position and momentum of an electron in a hydrogen atom [closed]

What can be expected as results for a set of position and momentum measurements of an electron in a hydrogen atom? I believe that for the position, we can expect something depending on the radial ...
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1answer
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Electron Capture or K-Capture and Heisenberg's Uncertainty principle

I read about Electron Capture or K-Capture in radioactivity. There I found that the electron in the K shell is captured by the nucleus and as a result the atomic number of the element decreases by 1 ...
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1answer
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What is velocity in QM?

I've always thought that velocity is the quantity $\vec v=\frac {d \vec x} {dt}$ by definition. That is, velocity is a quantity whose measurement is the above operation of the quantities $\vec x$ and $...
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1answer
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Uncertainty principle from QFT

Is it possible to derive uncertainty principle from QFT? Which kinds of perturbation (particles, monopoles, ...) are rule out by this principle?
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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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Why is $\Delta x$ or $\Delta p$ constant for a particular $\psi_n$?

We were asked to calculate $\Delta x \Delta p$ for the $\psi_0,\psi_1$ of the harmonic oscillator.And so we calculated the answers and verified that $$\langle T \rangle +\langle V\rangle = (n+1/2)\...
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1answer
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Is Heisenberg's uncertainty principle consistent with Special Relativity?

According to me, an object gains relativistic mass as it approaches the speed of light, and $$\Delta x \Delta p \ge\frac {\hbar}{2}$$ So objects with speeds close to $c$, should show less uncertainty ...
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1answer
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What is a fracton? [closed]

Recent, in articles on QFT and condensed matter new objects appear -- fractons. As I understand now, fracton is a particle with restricted motion: for example, such excitations can move only along ...
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3answers
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Do physical entities with one dimension equal to 0 exist?

Within mathematics, a lot of entities with one or more size equal to zero exist and are fluently manipulated. For example, within $\mathbb R^4$, the entity defined as $z=0, t=2$ is a plan, the one ...
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Heisenberg uncertainty principle in daily life

I need some examples of the Heisenberg uncertainty principle on a basic level, or if possible in daily life. Or maybe a simple explanation for validity of the principle in easier words. I cannot get ...
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4answers
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A question regarding the commutators of operators

Suppose we have got a triple of observables $A,B$ and $C$. Suppose furthermore, that $[A,B]=0$ and $[B,C]=0$ but $[A,C]\neq 0$ . Suppose, also now we do a measurement of $A$ then accordingly we would ...
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Can we measure $x$ and $p_x$ simultaneously by measuring $p_y$ and $y$ as well?

Suppose our plan is to measure experimentally the position $(x,y)$ in the plane and the momentum $(p_{x}, p_{y})$ of a quantum particle. Assuming the canonical commutation relation between $x$ and $p_{...
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Can we think about a particle trapped in a potential well in terms of “quantum measurement”?

Usually, when I'm thinking about a quantum measurement, I see a sort of particle that is being hit by a photon. The more energy the photon carries, the more the momentum of the particle is disturbed, ...
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Is the Uncertainty Principle a mathematical consequence or a physical consequence or both? [duplicate]

I am currently exploring the mathematical structure of Quantum Mechanics on an introductory level. A couple of books and online sources (including this website) stated how the Uncertainty Principle is ...
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What does the uncertainty principle tell us about the harmonic oscillator?

For the harmonic oscillator we have $\sigma_x \sigma_p = \hbar(n+1/2) $ and by the uncertainty principle $\sigma_x \sigma_p \geq \frac{\hbar}{2}$. In one of the exercises I was doing I was asked to ...
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What's the relationship between the definition of the uncertainty principle using standard deviations vs using $\Delta x$ and $\Delta p$?

So I've heard two different explanations of the uncertainty principle, both of which make sense on their own, but I'm having a hard time figuring out how they're connected. The first is that the ...
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How is the uncertainty principle related to the non-commutativity of the multiplication of operators in quantum mechanics? [duplicate]

The way I understand the uncertainty principle is that it's not even really about quantum mechanics specifically -- it's just a property of waves. e.g. A periodic wave doesn't even have a well ...
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Why cant we lower temperature to X where if an electron is observed it will be as if its an unobserved Temperate Y

Lets say the temperature is Y, and we want to observe an electron but if we do we will use a high energy light wave which will make it act more like a particle, so why dont we just lower the ...
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2answers
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Electronic component of the Hamiltonian operator and uncertainty principle

This question has to do with the concept of uncertainty principle. The Hamiltonian operator has the electronic component that takes the inverse of the distance between any two electrons. My question ...
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Deriving a uncertainty inequality

Starting from $$(Δx) (Δp) \geq h/2$$ How does one derive $$a^2 (Δx)^2 + (Δp)^2 \geq a h~? $$
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How can infinite sine waves localize to a single pulse in space?

I have heard countless times (and not just when discussing the Heisenberg's Uncertainty Principle) that making a short pulse using sine waves requires more and more sine waves to localize the pulse ...
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Different definitions of the uncertainty principle

In the book Introduction to Quantum Mechanics by Griffiths, the mathematical form of the uncertainty principle is stated as $$\sigma_x \sigma_p \ge \frac{\hbar}{2}.$$ However, another book on QM, that ...
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If particles like the $W$ boson can have a range of masses, can quarks and leptons also have a range of masses?

The reason why the weak nuclear force is weak is because the mediators, the $W$ and $Z$ bosons, need to take on a ridiculously high mass compared to the mass that they are usually found at (which is ...
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Contradiction with the uncertainty principle using repeated measurements

The uncertainty principle states that knowing the position of a particle with great accuracy would result in a very low certainty in the momentum of the particle. Suppose I have an experiment where I ...
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1answer
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Trying to prove Heisenberg's uncertainty wrong [duplicate]

Heisenberg’s uncertainty principle states that we cannot determine the position and momentum of a particle at a time. I think I have an idea to prove it wrong ( although I believe I must be wrong here)...
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1answer
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Complete set of commutating obsevables and Uncertainity Relation

In quantum mechanics, I read that when operators corresponding to observable commute, then they form a complete set that can define the state of the system. But in the case of $1$ dimension, we say ...
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What is the relationship between the uncertainty principle and electron diffraction experiment?

I know that the uncertainty principle says that we can't measure the position and momentum at the same time but I still can't relate it to the electron diffraction experiment. Isn't that the electron ...
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What happens to uncertainty in velocity with increase in velocity?

Heisenberg principle states that product of uncertainty in velocity (momentum but assuming mass constant) and uncertainty in position is greater than reduced Planck constant divided by 2. What happens ...
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Reasoning about the quantum mechanical characterization of energy

I have the Schrödinger equation: $$\dfrac{-\hbar^2}{2m} \nabla^2 \Psi + V \Psi = i \hbar \dfrac{\partial{\Psi}}{\partial{t}},$$ where $m$ is the particle's mass, $V$ is the potential energy operator,...
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Running couplings and the uncertainty principle

I stumbled across the Wikipedia article on coupling constants [1] and didn't quite unterstand, what the paragraph on running couplings is trying to express. It relates the virtual particles taking ...
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Uncertainty principle: $\Delta x \Delta p_x \ge \hbar/2$, where $p_x$ is the momentum in the $x$-direction

I am currently studying Diode Lasers and Photonic Integrated Circuits, second edition, by Coldren, Corzine, and Mashanovitch. Appendix A.1.1.1 says the following: In quantum mechanics, measurements ...
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Does $[A , B] \not = 0 $ necessarily mean $\Delta A \Delta B \ge k$ where $k \not = 0$?

For example : $[\hat{x},\hat{p}] = i \hbar \hat{I}$ and $\Delta x \Delta p \ge \hbar/2$ but in case of number states $|n \rangle $ $$[\hat{C},\hat{n}] = i \hat{S}\\ \Delta C \Delta n \ge 0 $$ where ...
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Entangled photons and CCD

Its a question about entangled pairs and double slit experiment. I have seen and read many such on the stackexchange but I can not really understand what is happening! So please don't stop the ...
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4answers
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Factor 2 in Heisenberg Uncertainty Principle: Which formula is correct?

Some websites and textbooks refer to $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ as the correct formula for the uncertainty principle whereas other sources use the formula $$\Delta x \Delta p \geq \...
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Uncertainty in wavelength of a photon emitted from atom

When an atom emits a photon, for some time the photon is close to its source, the atom, because it takes some time for the photon to move away from the atom. So during that time the uncertainty in the ...
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What is the actual uncertainty principle formula? [duplicate]

I found two different versions of the uncertainty principle in different books. In some it is written as $\Delta x\Delta p\ge\hbar$, while some others use $\Delta x\Delta p\ge\frac{\hbar}{2}$. I'd ...
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2answers
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What happens to the uncertainty principle if

I just read the Feynman Lectures about the electron gun experiment with two holes in the middle wall. It demonstrates that if we don't look at the electrons while they travel toward the detector ...
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Extension of uncertainty principle to mixed-states

In his Lectures on Quantum Theory, Isham states the generalized uncertainty principle for two observables $O_1$ and $O_2$ for a pure state $|\psi\rangle$ as $$\Delta_\psi O_1~\Delta_\psi O_2 \ge {1\...

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