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 a fracton?

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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Uncertainty of a system

Is the position-momentum of a system consisting of n particles equal to the sum total of the uncertainties of its constituent particles? If that is true, shouldn’t a macroscopic body have a very large ...
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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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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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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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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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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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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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Does Heisenberg uncertainty affect Snells law?

Assuming an ideal single frequency plane wave, we can determine the angle of retraction for the light beam. But the more I make my pulse shorter, the less certain I am in the frequency and thus the ...
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Looking for a very cheap heuristic demonstration (in a few lines) of Heisenberg inequality

While I perfectly know the true demonstration of Heisenberg uncertainty principle (from the full QM machinery), I'm looking for a very cheap heuristic way of getting $$\Delta x \, \Delta p \ge h, \tag{...
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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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Does the Heisenberg's uncertainty equation holds when one of the observable have zero variance?

From this link Heisenberg uncertainty principle, It says: Clearly, when $\Delta p_x$ shrinks, $\Delta x$ has to grow larger and larger in order to satisfy the Heisenberg inequality. For example, a ...
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Is every pair of conjugate variables associated with a Fourier transform?

For example, in quantum mechanics, the commutator of the position and momentum is $$[\hat{P_i} ;\hat{Q_j} ] =i\hbar\delta_{ij}\neq 0, i\neq j$$ I know that the position space representation of the ...
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Wave Nature of Matter in the Macroscopic World [duplicate]

Let us say that two macroscopic objects are at rest with respect to one another. Then we can see that $\Delta p$ is zero, because $v$ is zero. To compensate $\Delta x$ has to be infinity (according to ...
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TISE and uncertainty in energy

We use time independent schrodinger equation to find Stationary state solution for some potentials. My question is that, these Stationary state solutions are physically reliable or not? I am asking ...
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Can current and voltage be linked by an uncertainty relation when electrons tunnel through a barrier?

Quantum tunneling has been shown to be linked to uncertainty relations for some observables involved in the system. For instance, if we consider electrons tunneling through a potential barrier it can ...
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Heisenberg's Uncertainty Principle : How is particle position determined more accurately with shorter wavelengths? [duplicate]

In this principle, how can shorter wavelengths on the particle leads to determine more accurate position of the particle? I think it is somewhere related to reflection of the light from the particle, ...
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Why do we use ΔxΔp≥ℏ instead of ΔxΔp≥ℏ/2 to calculate the minimum uncertainty in momentum?

I came across a question in which we were asked to calculate the minimum uncertainty in the momentum of a particle. The solution showed that the min. uncertainty is found using the formula ΔxΔp≥ℏ ...
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Neutrino Helicity and Uncertainty

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase Neutrino are left-handed. The spin is in the opposite direction of motion. ...
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Quantum tunneling for bound states

In QM, take a particle in a bound state in $\mathbb{R}^n$ subject to a potential (need not be smooth and not necessarily bounded above, but is bounded from below, say, something that might roughly ...
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Why can't we directly measure the internal energy and entropy?

I learned about entropy in chemistry, I saw that we can measure $\Delta H$, but can't directly measure the $H$. So I searched about 'why we can't directly measure the '$H$'?', but I couldn't find the ...
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Designing an (thought) experiment to determine exact position

I know that Heisenberg's Uncertainty Principle prevents us from even theoretically predicting the exact position and momentum of a particle. There is always an uncertainty in one or the other, given ...
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Is monitoring CPU usage a good analogy of uncertainty?

There is a limit to how accurate measurement can be because making a measurement disturbs that which is being measured. This limit means there is inherent uncertainty in any measurement. When you ...
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Is it possible to explain the Quantum tunneling with the uncertainty principle?

I'm a high school student in South Korea(It is my first English question ever). I found descriptions of quantum tunneling with the uncertainty principle in Korea. There are two kinds of descriptions ...
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Applying uncertainty principle to energy states [duplicate]

Often for this I have heard, the longer the lifetime of the energy state, the uncertainty in the energy state decreases as a result of heisenberg's uncertainty principle. However doesn't that look at ...
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What Is the logic and the intuition of the Heisenberg Uncertainty Principle based on? Is it Quantum Superposition or on the electromagnetic spectrum? [duplicate]

With many sources on the internet it has sort of become diluted as to how and why the Heisenberg uncertainty principle still makes sense. One claims that it is due to quantum superposition and that a ...
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Is uncertainty uncertain?

I was thinking about uncertainty and wondered if uncertainty is inherently uncertain. I know in the uncertainty inequality for position and momentum, $\Delta x \Delta p \ge \hbar/2$, the presence of ...
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Does an electron have a fixed orbit in reality? [duplicate]

The Heisenberg's uncertainty principle prevents us from measuring the position and momentum of an electron accurately at the same time. But that is just our inability, right? In reality, would ...
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Why is it commonly said Angular momentum for ground state is zero (for system with rotation invariant potential)? [duplicate]

Neglecting any effect of spin,it is a well known fact,that orbital angular momentum of a system in ground state is zero.(For potential $V=V(r)$ .) The angle-angular momentum uncertainty,gives $\Delta{...
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1answer
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Is it possible to specify the position of a photon to arbitrary amounts? [closed]

For a photon, $$E = pc$$ from the Einstein Energy Equation. Or $$E = hf$$ with $$p = hf/c$$ From the Heisenberg uncertainty principle $$(\Delta x)*(\Delta p) = h/2$$ The maximum value for $\Delta ...
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(Another) Naive Question About Wavefunctions

I was recently introduced to wavefunctions in my freshman Modern Physics class. I understand that these waves do not- on their own- have a physical interpretation but the square of their magnitude ...
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Why must energy transitions in hydrogen atom be between stationary states?

In Griffiths QM textbook, he said that a hydrogen atom in the ground state may undergo a transition to some other stationary state by absorbing a photon. Why must this transition be to another ...
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Free Particle moving

My class finished the free particle dispersion derivation. Our professor asked us to, as an exercise, modify the derivation to fit a moving particle with a constant velocity. I think I managed it with ...

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