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.
227
questions with no upvoted or accepted answers
11
votes
1
answer
751
views
Which position and momentum distributions arise from some wave function?
Consider a particle in one dimension with wave function $\psi$. The probability density function describing how likely it is to find it in a given position is given by $f(x)=\left|\psi(x)\right|^2$. ...
- 895
5
votes
0
answers
175
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 ...
user17116
5
votes
1
answer
572
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 ...
- 466
5
votes
1
answer
2k
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 = \...
- 663
4
votes
0
answers
110
views
Uncertainty principle for incompatible observables whose probability distributions lack well-defined moments
The Heisenberg uncertainty principle states that the product of standard deviations (or variances) for incompatible observables has a non-zero lower bound (with a zero lower bound reserved for ...
- 342
4
votes
1
answer
168
views
Interfering alternatives and identical particles in Feynman and Hibbs
I am currently self-studying Feynman and Hibbs, and in his first chapter, Feynman talked about 'alternatives' like the various possibilities or paths an experiment can take. He defined two different ...
- 97
3
votes
0
answers
71
views
Is there some notion of classical uncertainty which quantizes to quantum uncertainty?
I would like to know if there is some notion of classical uncertainty which quantizes to give quantum uncertainty?
For instance, suppose we have a classical system whose phase space is given by a ...
- 549
3
votes
0
answers
130
views
$ΔqΔp \geq \frac{\hbar}{2}$ while $h$ is the cell in phase space
I can show how:
\begin{equation}
ΔqΔp \geq \frac{\hbar}{2}
\end{equation}
In a general way. You just need to consider the commutation properties of 2 generic operators to do so.
Both $p$ and $q$ ...
- 65
3
votes
2
answers
84
views
Is quantum uncertainty of particle location bound by the speed of light?
If I measure the location of a quantum particle and then measure its location 1 second later, is there a probability larger than zero that I find it in a location farther away from the first location ...
3
votes
0
answers
149
views
Proving the uncertainty relation for the quantum covariance matrix
In quantum optics papers we often encounter this version of the Heisenberg uncertainly relation (for an $n$-mode quantum system):
$\sigma + \iota \Omega \ge 0$
Where $\sigma$ is the covariance matrix $...
- 504
3
votes
0
answers
62
views
Quantum conditional von Neumann entropy - changing system I condition on, i.e. bipartite vs tripartite entropic uncertainty relation with qu. memory
I am reading Entropic Uncertainty Relations and their Applications by Patrick J. Coles, Mario Berta, Marco Tomamichel and Stephanie Wehner.
https://arxiv.org/abs/1511.04857
I am trying to reproduce ...
- 31
3
votes
0
answers
174
views
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 ...
- 119
3
votes
0
answers
138
views
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 ...
- 31
3
votes
0
answers
159
views
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 ...
- 2,004
3
votes
0
answers
206
views
Is there a Heisenberg Force?
If I read him correctly, in his book Quantum Theory, David Bohm argues that the reason an electron doesn't collapse into the nucleus is there is essentially a pressure due to the uncertainty principle ...
- 2,618
3
votes
0
answers
103
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 ...
user173730
3
votes
0
answers
951
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 ...
- 383
3
votes
0
answers
135
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 ...
3
votes
1
answer
259
views
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 ...
- 197
2
votes
0
answers
60
views
What does the Jacobi identity *mean* statistically?
Given that the commutator of a pair of operators shows up explicitly in the lower bound of the Robertson-Schrodinger inequality, I am wondering what, if any, statistical meaning/significance one can ...
- 18.9k
2
votes
0
answers
61
views
Can I use gravitational wave to break electron's double slit interference?
Electrons will perturb spacetime. So in principle in a double slit experiment, I can detect the gravitational wave emitted by the electron by a super-super capable detector at very far away, and ...
- 159
2
votes
0
answers
89
views
Informal derivation of the Unruh temperature
Imagine a charged particle of mass $m$ at rest in the electromagnetic vacuum.
The particle interacts most strongly with zero-point modes that have a wavelength $\lambda_C$ similar to the Compton ...
- 5,917
2
votes
1
answer
134
views
Confusion regarding the interpretation of simultaneity in the uncertainty principle
After studying the derivation of the generalised uncertainty principle, what I understand is:
Suppose we have two operators associated with observables $\hat{A}$ and $\hat{B}$. If I prepare a large ...
2
votes
0
answers
90
views
If position is fundamentally undefined at quantum scales, how can strings be Planck length?
From how I understand Quantum Mechanics and the Uncertainty Principle, quantum objects position is fundamentally undefined. So how could an object like a string with a clearly defined geometry exist ...
- 205
2
votes
0
answers
115
views
Why are commutators the first choice in describing observables that cannot be measured simultaneously?
In quantum mechanics, we convert Poisson brackets to commutators for the observables to account for the uncertainty principle. However, I do not understand why do we do this.
What motivates us to ...
2
votes
0
answers
136
views
Position/number uncertainty relation for the eigenstate of a Harmonic oscillator
Position and number operators for a Harmonic oscillator manifestly do not commute:
$$
\hat{n}=a^\dagger a,\\
\hat{x}=\sqrt{\frac{\hbar}{2m\omega_0}}(a + a^\dagger),\\
[\hat{x},\hat{n}]= \sqrt{\frac{\...
- 58.7k
2
votes
0
answers
76
views
What does it "physically" mean, in terms of uncertainty and measurements, for a commutator to be different than zero in quantum mechanics?
Let's consider the commutator $[L_i,L_j] = i \hbar L_k$ of the angular momentum. The consequence of this equation is that two components of the angular momentum cannot be simultaneously measured. I ...
- 97
2
votes
0
answers
95
views
Does the Kalman filter incorporate a Heisenberg-like uncertainty principle?
In the case of mechanical systems, applying the Kalman filter involves combining model based prediction (using an apriori known dynamical model) with real-world noisy observations of the positions and ...
- 2,392
2
votes
0
answers
63
views
Reference for HUP as Distinct from its Underlying Cause (i.e. Fourier Transform between Position and Momentum Space)
I am writing a paper for an applied optics journal and seeking a concise reference to help dispel the following misconception about how the HUP arises in quantum optics.
At one point i cite the ...
2
votes
0
answers
32
views
Deriving a uncertainty inequality
Starting from
$$(Δx) (Δp) \geq h/2$$
How does one derive
$$a^2 (Δx)^2 + (Δp)^2 \geq a h~? $$
2
votes
0
answers
214
views
Why does the uncertainty principle imply that empty space is filled with energy?
I read from this website that the uncertainty principle implies that seemingly empty space is filled with energy, called vacuum energy .
The relevant equation I can think of is $$\Delta E\Delta t \geq ...
- 4,215
2
votes
0
answers
307
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 ...
- 2,145
2
votes
0
answers
51
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
0
answers
182
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})...
- 94
2
votes
0
answers
356
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 ...
- 9,710
2
votes
0
answers
94
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 ...
- 675
2
votes
0
answers
91
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'...
- 177
2
votes
0
answers
189
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 ...
- 409
2
votes
0
answers
248
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
$$\Delta A| \alpha \rangle = \lambda \...
user101311
2
votes
0
answers
407
views
Simultaneous measurement of non-commuting observables without uncertainty
A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that $[\...
- 121
2
votes
0
answers
187
views
Uncertainty Principle - measuring momentum on one entangled particle, position on the other
If two entangled particles are sent far apart and then at exactly the same time the position of one, and the momentum of the other, is measured, won't this mean that, because the corresponding values ...
- 113
2
votes
0
answers
287
views
Uncertainty principle characterizing metallic bonding?
So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is:
$\Delta p \Delta x = \frac{\hbar}{2}$.
And ...
- 1,309
2
votes
0
answers
375
views
Momentum representation of a state
I am trying to figure out the momentum representation of the state which has the properties
$$\langle \psi |\hat q |\psi \rangle=-q_0,$$
$$\langle\psi|\hat p|\psi \rangle=p_0,
$$$$\Delta q\Delta p=\...
- 1,778
2
votes
0
answers
889
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 ...
- 125
2
votes
0
answers
134
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.
- 610
1
vote
0
answers
42
views
Photon and Observer effect
We cannot determine the position and momentum of a particle simultaneously with certainty . The product of uncertainty of them is greater than or equal to reduce planck's constant . The reason for ...
- 61
1
vote
1
answer
140
views
Uncertainties $\Delta r$ and $\Delta p_r$ for the hydrogenoid stationary states
I'm interested in the general formulas that give the exact uncertainties $\Delta r$ and $\Delta p_r$ (the radial momentum) for all stationary states $|n,l, m \rangle$ (or $\psi_{nlm}(r, \theta, \...
- 7,421
1
vote
0
answers
55
views
Is the space between plates, in Casimir effect, empty of momentum?
Please correct me if I am wrong. In Casimir effect, when two plates are brought very close to each other, there is a Force felt. This force is due to quantum fluctuations.
The space between plates is ...
1
vote
0
answers
46
views
Can I upper-bound uncertainties of $B$ in an eigenstate of $A$ using an appropriate norm of $[A,B]$?
There are times when I would really like a "reverse" uncertainty principle to hold, allowing me to upper-bound certain uncertainties in terms of properties of commutators. I'll try to ...
- 2,040
1
vote
0
answers
30
views
Connection between quantum non demolition measurement and the Heisenberg limit in metrology
Quantum non demolition measurements are those that do not feed back action noise into the measured observable. For discrete systems, this leads to the somewhat trivial case of where the observable (...
- 29