We’re rewarding the question askers & reputations are being recalculated! Read more.

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.

136 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
8
votes
0answers
2k views

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 ...
7
votes
1answer
528 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by $f(x)=\left|\psi(x)\right|^2$....
5
votes
0answers
143 views

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 ...
4
votes
1answer
66 views

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 ...
4
votes
1answer
1k views

Zero-point energy amplitude calculation

On this page https://www.miniphysics.com/simple-harmonic-oscillator.html It is stated that for a linear restoring force of $F = -k \Delta x$, the total energy is $ E = K + U $ or rather $ \\ E = \...
3
votes
0answers
58 views

Spin squeezing in quantum mechanics

The definition of spin squeezing in quantum mechanics is given as follows: Spin squeezing is a technique used to surpass the Standard Quantum Limit (SQL) of uncertainty in measurement (which for ...
3
votes
1answer
137 views

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 ...
3
votes
0answers
556 views

The Heisenberg Uncertainty in Bose Einstein condensates

What happens to the Heisenberg uncertainty principle, when a system reaches the Bose-Einstein condensed state? In our statistical mechanics lecture, we derived the following formula for the fraction ...
3
votes
0answers
100 views

Underlying C*Algebra operators in standard quantum mechanics?

Linearity in standard quantum mechanics (QM) is the key to making the math possible in this field, but the presence of nonlinear operators in QM is what is more generally dealt with. Working with the ...
2
votes
0answers
41 views

What is the characteristic of a property?

Background: The following two observations are , in my understanding, pretty much accepted in quantum theory: Location is a property which is not preexisting but is established by measurement. It is ...
2
votes
1answer
45 views

Measuring the Momentum of a Quantum System using Position Measurements

A basic way to measure the momentum of a charged particle is to know that (classically) it follows a circular trajectory in a uniform magnetic field perpendicular to the plane of its trajectory, with ...
2
votes
0answers
60 views

Are phase and particle (photon) number in QED conjugated variables?

I found in A. Zee's book "QFT in a nutshell" (1.edition) the interesting relation (8) respectively (9) in chapter III section 5 (p.173) which states that in a collective of non-relativistic bosons the ...
2
votes
0answers
53 views

Spread of the (smeared) field observable under time-evolution

Setup: Essentially, I'm interested in performing an analysis which is completely standard in QM, but I've never seen the analogue in QFT: Given I measure a system to have some value of its canonical ...
2
votes
0answers
84 views

In Cardy-Verlinde generalized uncertainty principle (GUP), how we know that the alpha is a constant of order one?

The GUP equation [1] is, $$\Delta x_i\geq\frac{\hbar}{\Delta p_i}+\alpha^2l_p^2\frac{\Delta p_i}{\hbar},$$ where $l_p$ is the Planck length. How do we know that $\alpha$ has a order of unity [1]? What'...
2
votes
0answers
131 views

Why is information conservation not restricted by the uncertainty principle?

The idea of information conservation seems to be: if all field equations/states of all particles/matter/waves at a certain time are known, all trajectories/waves can be backpropagated to retrieve all ...
2
votes
0answers
70 views

Connection Between Gaussian Fourier Transform and Minimal Uncertainty

The Fourier Transform of a Gaussian is a Gaussian. In QM, we get minimal uncertainty for a (normalized) Gaussian wave packet: $\Delta x\cdot \Delta p=\hbar /2$ Does the second fact has nothing to do ...
2
votes
0answers
103 views

QM result which implies equality in uncertainty relation

In Sakurai, there is a result in chapter 1 which states "the equality sign in the generalized uncertainty relation holds if the state in question satisfies $$\Delta A| \alpha \rangle = \lambda \...
2
votes
0answers
160 views

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 ...
2
votes
0answers
331 views

Calculating Natural Broadening of Emission Lines

I'm trying to demonstrate the small effect of Natural Broadening as compared to other types of broadening (Doppler, Stark, van der Waals, etc.) and my calculations don't match the accepted values. My ...
2
votes
0answers
243 views

The link between non-locality and Heisenberg's uncertainty relations

I have recently found out1 that the concepts of non-locality and Heisenberg's uncertainty do not live independently of one another in Quantum Mechanics. In other words, roughly the idea goes as: the ...
2
votes
0answers
294 views

Simultaneous measurement of non-commuting observables without uncertainty

A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that $[\...
2
votes
0answers
179 views

Uncertainty Principle - measuring momentum on one entangled particle, position on the other

If two entangled particles are sent far apart and then at exactly the same time the position of one, and the momentum of the other, is measured, won't this mean that, because the corresponding values ...
2
votes
0answers
206 views

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 ...
2
votes
0answers
306 views

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 p=\...
2
votes
0answers
663 views

Uncertainty Principle and Bohmian mechanics

The Uncertainty Principle is a relationship between measurements of pairs of attributes, position and momentum, as well as energy and time. Perfect precision of one attribute's measurement leads to a ...
2
votes
0answers
108 views

commutator to entropy in an uncertainty relationship?

Question: Does there exist a commutator to entropy in an uncertainty relationship? Similar Energy and time for instance.
1
vote
0answers
83 views

Derivation of mass-lifetime relation in particle physics

How is the inverse relation between the lifetime and mass of a virtual particle derived? For example, it is said that the strong force is short range because its force carrier is massive, and hence ...
1
vote
0answers
23 views

Defining Angle between Observables consistently

Problem Setup: There is a nice proof of the heisenberg uncertianty principle using cauchy-schwarz given here Stated in variance form it is: $$ \sigma_x^2 \sigma_p^2 \ge \frac{\hbar^2}{4} $$ Now ...
1
vote
0answers
60 views

The validity of some “applications” of the uncertainty principle

Given a $L^2$ function $f$ with $\int_\mathbb{R}xf(x)dx=0$, define its variance to be $\sigma_f^2=\int_{\mathbb R}x^2f(x)dx$. The uncertainty principle states that $\sigma_f\sigma_\hat f\geq 1/4\pi$,...
1
vote
0answers
21 views

Derivation of Margolus-Levitin bound on the Quantum Speed Limit

In their derivation of the Margolus-Levitin bound on the "quantum speed limit" the authors make use of a trigonometric inequality $\cos x \ge 1-\frac{2}{\pi}(x+\sin x), \quad \forall x\ge0$ Is ...
1
vote
0answers
61 views

Hawking temperature, uncertainty principle and size of a black hole

I was playing with the Hawking temperature formula $$T_H = \frac{\hbar\ c^3}{8 \pi\ G\ M\ k_B}$$ and I thought it would be interesting to associate a velocity to this temperature: $$k_B\ T_H = \frac{1}...
1
vote
1answer
34 views

Heuristic for large $x$ behavior from small $q$ behavior of Fourier Transform

If I have a function $h(\mathbf x)$ which may be written $$h(\mathbf x)= \int \frac{\text{d}^d\mathbf q}{(2\pi)^d} \, h(\mathbf q) e^{-i \mathbf q \cdot \mathbf x}$$ and assume spherical ...
1
vote
0answers
64 views

Does uncertainty principle truly represent the “lower bound” of the information we can obtained from a pair of noncommunicable operator?

Background I: Suppose the commonly used non commuting operator $\hat p$ and $\hat x$. The uncertainty principle told us that $\sigma_p\sigma_x\geq \frac{\hbar}{2}$. In standard quantum mechanic ...
1
vote
1answer
20 views

Length and velocity of a pulse of particles

We are given a pulse of protons of duration $10^{-7}s$ and energy $2KeV$. I know I am supposed to use the uncertainty principle to solve this. I need to get the length and the indetermination of the ...
1
vote
0answers
37 views

Confused about using uncertainty principle to determining momentum

A question asks to estimate the energy of a neutron, if the neutron is composed of a proton and electron by using the uncertainty principle. The basic idea is to let x = 1 fm and calculate p using: $...
1
vote
2answers
69 views

What happens to the uncertainty principle when I have a particle contained within an inelastic box?

Say I have a box made of inelastic material such that when a particle hits the box, energy is lost through heat. I then put a particle inside of this box and squeeze the box down. How does this not ...
1
vote
0answers
87 views

Where this interpretation for the field modes comes from?

I'm reading the book "Modeling Black Hole Evaporation" by Alessandro Fabbri and Jose Navarro-Salas, and in section 3.3.2 they talk about wavepackets at $\mathscr{I}^+$. It all starts like this: one ...
1
vote
1answer
37 views

What does Hawking mean by “in empty space the field can’t be fixed at 0 because then it’d have both a precise value and a precise rate of change of 0”

Slightly modified the language in the title to make it fit in 150 characters. The above comes up in the part leading up to the explanation of how black holes emit particles.. My impression was that ...
1
vote
0answers
44 views

How to get the Number Phase Uncertainty relation from the Energy time relation?

I can arrive at $\Delta H\Delta t \geq \frac{\hbar}{2}$, but how do I get from there to $\Delta N\Delta \phi \geq 1$ for the number states of light? I know we write $H = \hbar \omega (N + \frac{1}{2})...
1
vote
0answers
82 views

How does Heisenberg's uncertainty work with more than one quantum field?

How does Heisenberg's uncertainty principle work with more than one quantum field? I am specifically asking about the time-energy uncertainty: $$\Delta E \Delta t \ge \frac {\hbar}{2}\tag{1}$$ Imagine ...
1
vote
1answer
39 views

How can the derivation of the energy of an electron in a Fermi gas using the Heisenberg uncertainty principle be made rigorous?

When modeling a large number of non-interacting identical fermions in a potential well of volume $V$ as a harmonic oscillator and assuming the Pauli exclusion principle, it is easily seen that the ...
1
vote
0answers
63 views

The uncertainty principle and probing small scales

The uncertainty principle states that $\Delta x\Delta p \geq \frac{\hbar}{2}$. So if you know momentum to high precision, you can't know position to high precision. In the context of accelerator ...
1
vote
1answer
67 views

What is the relation between uncertainty and information obtained from a measurement?

For ex. if a measurement gives a position with twice the uncertainty as another measurement, how much less information regarding position are you getting? In other words, if uncertainty doubles, is ...
1
vote
1answer
56 views

Potentials and position uncertainty

In the Schrodinger equation, we have some potential $V(x)$. But generally, there is some uncertainty in the position with solutions to Schrodinger's equation. Classically, we would say that a particle ...
1
vote
0answers
31 views

Implications for QM of “Photoionization in the time and frequency domain”

"Photoionization in the time and frequency domain", a recent paper published in AAAS Science, purportedly falsifies the Heisenberg Uncertainty Principle. Quoting the ScienceDaily article on this ...
1
vote
0answers
89 views

Indeterminacy in Quantum Mechanics

Heisenberg's uncertainty principle tells us that there is a lower limit on the accuracy with which we can determine both the momentum and the position of a particle simultaneously. $\Delta$$x$ $\...
1
vote
1answer
81 views

Wave function collapse, EPR paradox and information transfer

For a classical formulation of the EPR paradox, two particles are produced, with total momentum zero and separated by a long distance. So say we measure the momentum of one particle first, and measure ...
1
vote
0answers
63 views

Does the Robertson uncertainty relation concern the same quantum system?

Does the Robertson uncertainty relation concern the same quantum system? Ie. should the observables $ A, B$ be measured on the same system or can they be measured on two independent systems? I have ...
1
vote
0answers
68 views

Commutator implies division of phase space in cells of area $h$?

There is a detail from a very well-written answer here that interested me. Unfortunately Springer is charging 41 Euros to access the paper cited by the author. I wonder if someone could elaborate on ...
1
vote
1answer
77 views

Energy of a particle

When a particle such as an electron borrow energy to overcome a physical barrier, ( according to Heisenberg principle ) that energy has to be returned after a short while. Since total or a part of the ...