This tag is for Heisenberg quantum mechanical uncertainty principle.

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How can a clock work if the uncertainty principle is true?

If the uncertainty principle and Copenhagen Interpretation are true, then how can a clock tick? Supposedly particles can do all sorts of things when not measured, then how can they be formed into ...
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Uncertainty principle in Quantum mechanics

The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously. Is this because the uncertainty is the natural characteristic or it is ...
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How do you measure a particle's postion or momentum?

This question is about the Uncertainty Principle $$\sigma_x \sigma_p ~\ge ~\frac{\hbar}{2}.$$ Looking at the maths, I understant why the uncertainty in the poistion increases as the uncertainty in ...
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Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
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The Uncertainty Principle and Energy Nonconservation

The uncertainty principle is listed in most textbooks and articles as $$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$ This can be derived in many ways in many different settings, most of them involving ...
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Does measuring the exact position of a ball destroy the ball

If you have a macroscopic ball (say, a tennis ball) and you (hypothetically) try to measure the exact position of the center of that ball by measuring the exact positions of the atoms making up the ...
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Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
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438 views

Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
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What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's ...
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Heisenberg's uncertainty principle - Planck's (reduced) constant divided by two or not? [duplicate]

The most common form of Heisenberg's uncertainty principle I've seen online is $$ \Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$ However, I also regularly see $$\Delta x \Delta p ~\geq~ \hbar. $$ ...
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Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes ...
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Relating Schrödinger's Wave Equation and Heisenberg Uncertainty Principle

A homework question that I don't conceptually understand: A quantum particle of mass M is trapped inside an infinite, one-dimensional square well of width $L$. If we were to solve Schrodinger's wave ...
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Doesn't the uncertainty principle mean all particles with identical energy are indistinguishable and hence have an amplitude for exchange?

I wonder if someone could tell me where my logic is going wrong here? If two particles both have definite energy, then they have indefinite position. As their positions could literally be anywhere ...
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Quantum entanglement and uncertainty

I have a question about measuring entangled particles and the uncertainty principle. I know that this has been asked before, but I am still not clear on the explanations, so I will try to explain why ...
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270 views

Energy of quarks and the mass of the proton

We know that energy of quarks inside the proton can not be exactly fixed because if it,the 'proton decay' must not be exist. My question is if the energy of quarks inside the proton is not exactly ...
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Is the uncertainty principle axiomatic or derived?

To take an example, Feynman Lectures Vol 3 13-1 Let's think of an electron which ban be in either one of two positions [...] There are two possible states of definite energy for the electron. ...
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Does the uncertainity principle violate the law of conservation of energy?

What is the scientific view of the beginning of universe? Quantum fluctuation seems to contradict with the law of conservation of energy. Uncertainity Principle does seem to violate the Law of ...
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Uncertainty principle and commutation relations [duplicate]

What connection exists between the uncertainty principle and commutation relations amongst the operators representing observables in Quantum Mechanics?
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Momentum representation of a state

I am trying to figure out the momentum representation of the state which has the properties $$\langle \psi |\hat q |\psi \rangle=-q_0,$$ $$\langle\psi|\hat p|\psi \rangle=p_0, $$$$\Delta q\Delta ...
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Gaussian Probability Distribution?

The uncertainty principle states that, $$\sigma _{{x}}\sigma _{{p}}\geq {\frac {\hbar }{2}}.$$ It is mentioned from many sources that the probability distribution of the particle position and ...
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Is it only the ground state of the quantum harmonic oscillator that has the minimum uncertainty product?

We know that the uncertainty product of general states is bounded by the inequality described by Heisenberg's uncertainty relation. And the ground state of the quantum harmonic oscillator falls under ...
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70 views

Theoretical Upper Bound on Processor Speed?

Barring aside considerations such as heat dissipation, capacitance, etc... (aka any sort of technological issue) what is the fastest speed of a processor? I am told that at distances of 1 planck ...
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Intuitive explanation for angular momentum uncertainty?

The basic commutator relation $$[J_1,J_2]=i \hbar J_3$$ of quantum mechanics yields the uncertainty relation $$\Delta(J_1)\Delta(J_2)\ge \frac{\hbar}{2}|\langle J_3\rangle|.$$ However, unlike the ...
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260 views

Can Zeno's Dichotomy Paradox be Resolved with Quantum Mechanics?

I would like to start off by saying this is not a philosophical question. I have a specific question pertaining to physics after the following explanation and background information, which I felt was ...
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Physical meaning of uncertainty principle + question on symmetry

A question on the Uncertainty principle. So we know that it says (for position and momentum) that: $$ \Delta x \Delta p \ge \hbar/2 $$. Where $\Delta p = \sqrt {<p^2> - <p>^2 }$ and ...
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Finding $\Delta p$ for discontinuous wave function

So I have a triangle Wavefunction defined as: $$\psi(x)=\begin{cases}x &0<x<\frac{L}{2} \\ L-x &\frac{L}{2}<x<L\end{cases}$$ When I try to find the uncertainty in momentum, I ...
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Quantum Mechanics and General Relativity in Macroscopic Level [duplicate]

Hi I read a book yesterday.The book was Brian Greene's The Elegant Universe. I learned that uncertainty principle affects space-time very microscopic levels and this affection makes conflict in ...
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Quantum state with zero standard deviation of position operator

Is any quantum state $|\psi\rangle$ possible such that the standard deviation $\sqrt{\langle\psi|(\Delta\hat{x})^2|\psi\rangle}$ of the position operator $\hat{x}$ is zero? If not, why?
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Uncertainty on a single observable measurement

Heisenberg Uncertainty Principle states (in the form of the Robertson-Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement ...
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On an Uncertainty Relation for Angular Variables

I'm looking for a proof of the Angular Momentum - Angle uncertainty relation $$\frac{\Delta L \Delta \theta}{1-(3/\pi^2)\Delta \theta^2} \geq \frac{\hbar}{2}$$ which does not involve solving the ...
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From where does a particle get the energy to tunnel?

When a particle is made to confine more and more to a particular position it breaks the energy barrier to get out because of the uncertainty principle. But, from where does the particle get the energy ...
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207 views

Heisenberg uncertainty principle and minimum energy

In an exercise, given the average lifetime $\tau$ of a particle, the author estimates the minimum energy using the uncertainty principle formula : $\Delta E \Delta t \geq \hbar/2$, assuming $\Delta t ...
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dispersion relation in presence of a potential

Let there be a particle in a step potential: if its energy $E$ is higher than the step $V_0$, then it will have the momentum $\sqrt{2m(E-V_0)}$ and no more $\sqrt{2mE}$. (See ...
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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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Heisenberg relation

Given that $A(k)=\frac{N}{k^2+\alpha^2}$, show that $\Delta k \Delta x >1$. Considering the above example, according to my textbook, it is written that I must square the above function and ...
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Why complex functions for explaining wave particle duality?

I have this very bad habit of going to the scratch, discarding all the developments of a theory and worldly knowledge, and ask some fundamental (mostly stupid and naive, as some may say) questions as ...
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Heisenberg's uncertainty principle - $ \Delta p $

So I was reading this paper, "Limits to Binary Logic Switch Scaling—A Gedanken Model". The following is the paper's abstract: In this paper we consider device scaling and speed limitations on ...
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Light pulses and energy-time uncertainty principle [duplicate]

Suppose we have a monochromatic light beam. We put an obstacle between source and observer and remove it repeatedly by certain frequency such that observer sees an oscillating intensity of light. Will ...
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Why is the Bohr's idea of defined circular orbits overruled?

If we consider a thought experiment for determining position of an electron by using photons of light. According to principles of optics, if we use light of wavelength $\lambda$, then the position of ...
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Understanding the virtual states referenced in multiphoton absorption studies

The Heisenberg energy-time uncertainty tells us that we can have so-called virtual states between eigenstates as long as the lifetime of these states is at most: $\tau = (\frac{h}{4 \pi E_v})$ Where ...
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In calculations with uncertainty principle why could you equate the uncertainty in momentum with the actual momentum of the system

This website is trying to calculate the confinement energy of a electron starting from the uncertainty principle, but it does this: $\Delta p=p$. Why is this valid?
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Does the uncertainty principle make simulation of systems impossible?

Is it possible to fully define a system, then be incapable of simulating or calculating its future states due to the Uncertainty Principle? If it can be done, how?
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Why $\Delta x \Delta p_x$ for stationary states increase linearly with n?

Harmonic Oscillator $\displaystyle \Delta x\Delta p_x = \hbar (n+\frac{1}{2})$ Particle in a box $\displaystyle \Delta x\Delta p_x = \frac{\hbar}{2} \sqrt{(\frac{n^2\pi^2}{3}-2)}$ We notice ...
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Why the uncertainty principle can be used for estimation?

It is usually said/done in textbooks and classes that if $\Delta x$ is known then $\Delta p_x$ can be estimated using the uncertainty principle as $\Delta p_x \sim \hbar/\Delta x$. But the ...
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Estimating minimum energy with uncertainty principle

I'm currently trying to solve a problem that involves estimating the minimum energy of a particle in the potential: $$ V(x) = \frac{-V_0a}{|{x}|} $$ I'm quite confused about how to handle the ...
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366 views

Is uncertainty principle a technical difficulty in measurement?

I have searched for an answer to this question on physics SE but I have not seen a question in which it is addressed properly. Please let me know if there is an answer already. My question briefly ...
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5answers
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Why does the universe follow the uncertainty principle?

I have been thinking about this question for quiet a long time but, couldn't make up an answer myself. Usually when someone asks about why a system is the way it is we answer it by saying that it is ...
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320 views

How to derive the uncertainty relation for a system of arbitrary potential?

I've been trying to understand the derivation of the uncertainty principle for the harmonic oscillator as described here (see pages 100-101). What I don't understand is how the potential for the ...
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Photons vs Uncertainty Principle

The uncertainty principle states: $\Delta_x\Delta_p>ħ/4$ We know the photon has a 0 rest mass but we are say that it's momentum is always the same $e=pc$ And more we are certain about the ...
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Uncertainty principle in atomic clocks?

How does the uncertainty principle limit the accuracy of atomic clocks. I know line width and measurement time are important but not exactly why?