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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How does the uncertainity principle apply in this situation?

A common (but, as I think, incomplete) description of the uncertainity principle is the following: You cannot determine a particle's momentum and position at high accuracy at the same time It could ...
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Probability question based on Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle relates energy and life time $\tau$ of a particle as follow: $\tau=\frac{\bar{h}}{1+x^2}$ Here energy is approximated as $1+x^2$ where $x$, the velocity of particle, ...
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Does the uncertainty principle say that conservation of momentum is violated in quantum mechanics? [duplicate]

The uncertainty principle of Heisenberg says that the uncertainty in the position of a particle multiplied by the uncertainty of the momentum of a particle is always more than or equal to $\frac{\hbar}...
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Uncertainty principle in relativistic quantum mechanics

In Walter Greiner book about relativistic quantum mechanics, he writes the uncertainty relations for 4-position and 4-momentum in a neat way as: $$[p^\mu, x^\nu] = i\hbar \eta^{\mu\nu}{\bf 1}$$ with ...
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Classical vs quantum definition of observables

Let's suppose the probability distribution for position of a particle is very sharply centered about 0. Then surely I know it has little deviation about the mean? If it has little deviation about the ...
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1answer
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Prove: $(\Delta x)(\Delta \lambda) \geq \frac{\lambda^2}{4\pi}$

Currently I was going through the formula $$(\Delta x)(\Delta p)\geq\frac{h}{4\pi}$$ which is of course the enclosed form of Heisenberg’s Uncertainty Principle. But I also get this formula $$(\Delta x)...
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Do electron-electron collisions have an associated scattering cross section?

Various texts (1,2) state that electrons are point particles, but if this is the case then when two electrons collide, one of them knows the others position with exact certainty (treating one as an ...
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Uncertainty principle fundamental or not? [duplicate]

The Heisenberg uncertainty principal says we cannot currently precisely measure position and momentum of a particle. So in principle and one day if we figure out how, or have more better sensitive ...
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On the interpretation of Heisenberg's principle

This question (hoping it's not completely irrelevant) is about the interpretation of Heisenberg's principle and a ficticious opposite to the relation. $$\sigma_x \sigma_p \geq \frac{\hbar}{2}$$ I'm ...
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Why is the anticommutator of the uncertainty principle omitted if it serves to increase the accuracy of our “knowledge” of a quantum state?

The generalized uncertainty principle can be derived and shown to be this which is fine and rigorous. $\langle ( \Delta A )^{2} \rangle \langle ( \Delta B )^{2} \rangle \geq \dfrac{1}{4} \vert \langle ...
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Uncertainty Principle state space of a single particle/object?

My question is about mathematics in the context of physics Imagine a series of quantum states of a single particle: In the first state the particle has a certain position but an uncertain momentum In ...
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Why doesn't Gaussian wavepacket broadening in position mean there will be a shortening in momentum?

Many sources that say in free broadening of a Gaussian wavepacket, the momentum uncertainty (I think defined in terms of the range of 'significant' momentum amplitudes) is time invariant even as the ...
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Can Schrödinger's cat be filmed?

Before opening the box, the observer does not know if the cat is alive or dead, however, a camera placed internally "knows" all the time, which is really happening. Does this camera cancel ...
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Can neutrinos be entangled in their oscillations?

If two neutrinos are entangled somehow--say, for instance, by being created in the same reaction--would their flavor (Tau, Muon, Electron) be enangled, including in their oscillations between the ...
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Does the uncertainty $\Delta \hat a$ of the annihilation operator of the harmonic oscillator remain constant over time?

I'm supposed to prove that the uncertainty of the annihilation operator of the harmonic oscillator, given by $$\Delta \hat a=\sqrt{\langle\hat{a}^{2}\rangle-\langle\hat{a}\rangle^{2}} \tag1$$ doesn't ...
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Is “borrowed energy” less available elsewhere?

W and Z bosons have large masses, but they can still come into existence for short periods of time by "borrowing" energy from the vacuum. When this energy is borrowed and the particles come ...
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If Heisenberg's uncertainty principle is an inherent property of nature, why does Heisenberg's microscope indicate an observation-based experiment? [closed]

I am aware of this SE-Answer, however, I am eager to know why Heisenberg himself introduced an observation-based experiment to demonstrate his intuitive explanation of his uncertainty formula. Does ...
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Does electron orbital theory contradict the Heisenberg uncertainty principle?

The quantum-mechanical model of atoms was derived from Heisenberg's uncertainty principle, which states that the position and momentum of a particle cannot both be determined to an arbitrary degree of ...
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Does position-momentum uncertainty principle apply to a two-body wavefunction when we frame boost to its center of mass reference frame?

The heart of my question is below in bold. The rest is clarifying information or additional points of discussion - in case my assumptions are the heart of my misunderstanding. In a two body attractive ...
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1answer
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Conservation of momentum in single slit experiment

I am reading about the uncertainty principle and its stated that we can not simultaneously determine the position and momentum of a photon. But my question is, if you know the initial momentum of the ...
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Regarding Heiseberg's microscope experiment

In the above picture of the microscope experiment, I am considering that the observer is situated at the eyepiece. The observer is a rectangular 2D grid of square-shaped detectors, each detector with ...
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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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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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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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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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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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5answers
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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