This tag is for Heisenberg quantum mechanical uncertainty principle.
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Why is the expectation value of the Hamiltonian/position commutator equal to zero?
I know that the commutator $[H,x]$ is $-i \hbar \,p/m$, but how do I show that the modulus of the expectation value of this is zero?
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4answers
261 views
An entropy of the Wigner function
Is there an entropy that one can use for the Wigner quasi-probability distribution?
(In the sense of a phase-space probability distribution, not - just von Neumann entropy.)
One cannot simply use ...
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1answer
47 views
Uncertainty Principle on System of particles
I am new to Quantum Mechanics. I read the uncertainty principle - it says there are pairs of physical quantities which can't both be determined with certainty for a particle.
My question is does the ...
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1answer
54 views
Why is the Heisenberg Uncertainty Principle not obvious give the conservation of mass- energy?
A photons energy is given by $E=h *f$ and momentum $p=E/c$ (spin?) but the photon has no (rest) mass! Therefore it is the ultimate probing tool for looking at any mass position and velocity because ...
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Does quantum mechanics depend solely on electromagnetic waves? [duplicate]
I am beginning to learn quantum mechanics. Since determining the position of an object involves probing by electromagnetic waves and since i have read a simple derivation of Heisenberg's uncertainty ...
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1answer
76 views
Uncertainty-principle and the Maxwell formalism of electromagnetic waves
An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" ...
3
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1answer
123 views
Phase space in quantum mechanics and Heisenberg uncertainty principle
In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state.
In my book about statistical physics ...
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3answers
100 views
Reaching the speed of light via quantum mechanical uncertainty?
Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- ...
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1answer
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Connection between a simple matter wave and Heisenberg's uncertainty relation
When looking at the wave function of a particle, I usually prefer to write
$$
\Psi(x,t) = A \exp(i(kx - \omega t))
$$
since it reminds me of classical waves for which I have an intuition ($k$ ...
4
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1answer
72 views
Simple uncertaintly calculation of the center coordinates of a Landau Level
I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long.
In equation 2.39, the ...
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1answer
45 views
Heisenberg's uncertainty and $0 K$ temperature
when a body is subjected to $0 K$ temperature, it becomes rigid. hence if we see in terms of quantum the lattice vibration decreases, resulting in no change in the direction of the Random velocity, ...
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3answers
493 views
Observation of violation of the uncertainty principle?
I stumbled upon this piece of news in the BBC's website http://www.bbc.co.uk/news/science-environment-19489385, discussing this paper
http://prl.aps.org/abstract/PRL/v109/i10/e100404, which reports ...
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2answers
98 views
Do viruses suffer from quantum de-localization?
Consider some microscopic life form. It should obviously be localized in space, in the quantum-mechanical sense, if it is treated as a single particle (though it is composite). If its characteristic ...
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General physics question involving Heisenberg Uncertainty Principle
Question:
An unstable particle produced in a high-energy collision is measured to have an energy of $483\ \mathrm{MeV}$ and an uncertainty in energy of $84\ \mathrm{keV}$. Use the Heisenberg ...
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1answer
70 views
Uncertainty Principle and Energy range for an electron in an atom
I have the following exercise:
Use Heisenberg's uncertainty principle and the relation $\Delta u = \sqrt{\langle u^2 \rangle - \langle u \rangle^2}$ to find the range of energy an electron has in an ...
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1answer
76 views
Uncertainty and Thermodynamics
Dilemma
The uncertainty principle of energy and the 2nd law of thermodynamics don't add up : the uncertainty principle of energy says that
$\Delta \tau \cdot \Delta E \ge \frac{h}{4\pi} = ...
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1answer
60 views
Why uncertainity is minimum for coherent states?
While reading for quantum damped harmonic oscillator, I came across coherent states, and I asked my prof about them and he said me it is the state at which $\Delta x\Delta y$ is minimum. I didn't ...
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3answers
338 views
How Uncertainty Principle, Vacumm fluctuations and Energy Conservation coexist in QFT?
Recently I had a debate about the uncertainty principle in QFT that made me even more confused..
Because we use Furrier transforms in QFT we should have an analogue to the usual Heisenberg ...
3
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4answers
185 views
Are photons deterministic?
I propose the following scenario:
At $t=0$, a photon is emitted from a star. At $t=n$, said photon is received and interpreted by some detector.
My question is whether or not it is accurate to say ...
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1answer
116 views
Exploiting the Heisenberg Uncertainty Principle as a means to communicate
It seems as though I've come across a rather unusual conclusion that could either simply be a misinterpretation or a contradictory discovery. I seem to have found a way to utilize the Heisenberg ...
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2answers
77 views
About Heisenberg uncertainty principle [duplicate]
What would happen if someone invented a way to measure both position and momentum precisely? If it is impossible why?
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3answers
114 views
Couldn't we measure electrons with good enough technology? [duplicate]
I am a bit confused about the Heisenberg's Uncertainty Principle - just read about it in How to Teach Physics to Your Dog, by Chad Orzel. He states that the reason electrons can't be measured is ...
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1answer
44 views
Velocity of measurement
As per to Heisenberg uncertainty we will not be able to calculate the position and momentum at same instant because by the time we calculate the next of the one, it changes (i.e.) the changes are very ...
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1answer
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Experimental perspective in understanding the Heisenberg Uncertainty Principle
I need to confirm whether or not I understand Heisenberg Uncertainty Principle. So the crucial thing is that you need an "ensemble" of measurements:
$$\delta x \delta p \ge \frac{\hbar}{2}.$$
If I ...
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2answers
324 views
The Uncertainty Principle and Black Holes
What are the consequences of applying the uncertainty principle to black holes?
Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
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6answers
315 views
Why is Heisenberg's uncertainty principle not an experimental error since it is the error created by photons striking on elementary particles?
Why is Heisenberg's uncertainty principle not an experimental error since it is the error created by photons striking on elementary particles?
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Isn't the uncertainty principle just non-fundamental limitations in our current technology that could be removed in a more advanced civilization?
From what I understand, the uncertainty principle states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on ...
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3answers
229 views
Why can't we use entanglement to defy Heisenberg's Uncertainty Principle?
In principle, it is possible to entangle any property of two particles, including speed and momentum. Surely then, this could be used to defy the Uncertainty Principle, which states that the momentum ...
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1answer
209 views
Is there any uncertainty between mass and proper length or time?
I was trying to naively draw a parallel between special relativity and the Heisenberg uncertainty principle. I try to understand uncertainty principle as a consequence of 4-position and 4-momentum ...
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1answer
128 views
Absolute zero and Heisenberg uncertainty principle
I got to read Feynman vol I and there was written that at absolute zero, molecular motion doesn't cease at all, because if so happens, we will be able to make precise determination of position and ...
5
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3answers
176 views
Does a ball thrown in the air really stop at its apex, and if it does, wouldn't that violate the uncertainty principle?
When throwing a ball straight up, most experts say that it momentarily comes to a stop at its apex before its return fall. If it stops, wouldn't we know its velocity and position and wouldn't this ...
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3answers
165 views
Do electrons have definite and single value of momentum and position?
Do electrons (individually) have definite and single value of momentum and position or do they simultaneously have multiple position (a spread) at a time?
In other words, according to the uncertainty ...
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2answers
592 views
Why is the Heisenberg uncertainty principle stated the way it is?
I spent a long time being confused by the Heisenberg uncertainty principle in my quantum chemistry class.
It is frequently stated that the "position and momentum of a particle cannot be ...
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1answer
183 views
In QM, does random data “come from anywhere”? Also, what are the properties of the data?
I have only taken a basic quantum mechanics course (this book, so you know where I'm coming from), but I've been wondering about something.
If we set up a quantum system in a known state and take a ...
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2answers
258 views
Heisenberg uncertainty principle derivation - unexplained factor of $4 \sigma_k^2$ in Gaussian
I did a Fourier transform of a gaussian function $\scriptsize \mathcal{G}(k) = A \exp\left[-\frac{(k-k_0)^2}{2 {\sigma_k}^2}\right]$
$$
\scriptsize
\begin{split}
\mathcal{F}(x) &= ...
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3answers
180 views
Is it possible for $\Delta x$ ($\sigma_x$) of any free particle wave packet to be decreasing at any time?
Consider any wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens ...
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1answer
344 views
Gaussian wave packet
At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves $\psi = \psi_0(k) e^{i(kx - \omega t)}$ over wave numbers $k$. We do it at $t=0$ hence $\psi = ...
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3answers
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Proof of Canonical Commutation Relation (CCR)
I am not sure how $QP-PQ =i\hbar$ where $P$ represent momentum and $Q$ represent position. $Q$ and $P$ are matrices. The question would be, how can $Q$ and $P$ be formulated as a matrix? Also, what is ...
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Is the uncertainty principle just saying something about what an observer can know or is it a fundamental property of nature?
I ask this question because I have read two different quotes on the uncertainty principle that don't seem to match very well. There are similar questions around here but I would like an explanation ...
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5answers
300 views
What is $\Delta t$ in the time-energy uncertainty principle?
In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
3
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2answers
350 views
Calculating lifetime of a pi meson via Heisenberg uncertainty relationship?
This is a problem from my textbook:
"A proton or neutron sometimes 'violates' conservation of energy by emitting and then reabsorbing a pi meson, which has a mass 135MeV/$c^2$. This is possible as ...
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1answer
81 views
Quantum entanglement, quantum measurement, spin and position
By uncertainty principle, we know that determining particle's position at some location is limited. So we cannot determine the position of a particle at some exact point location as this would make ...
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6answers
627 views
What constitutes an observation/measurement in QM?
Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle.
What is the technical definition of an observation/measurement?
If I look at a QM system, it ...
3
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1answer
341 views
Physical Significance of Fourier Transform and Uncertainty Relationships
What is the physical significance of a fourier transform?
I am interested in knowing exactly how it works when crossing over from momentum space to co ordinate space and also how we arrive at the ...
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1answer
154 views
Uncertainty relation and Energy-Position interference
How would you prove that the simultaneous measurements of position and energy are not subject to interference?
I was thinking in calculate the commutation relation between $x$ and $H$ (Because $\Delta ...
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1answer
111 views
Semiconductors and localization of the electrons
When looking at the band diagram of a semi-conductor, direct conclusion of the invariance under discrete translations, for a filled state with an electron, one does know precisely it's momentum, so my ...
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1answer
159 views
Why shouldn't the uncertainty principle be interpreted as an observer effect?
The Heisenberg Uncertainty Principle suggests that the more precisely the position of a particle is measured, the less precisely its momentum can be known, and vice versa.
$$\sigma_x \sigma_p \geq ...
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2answers
170 views
How does QM allow imaging of individual electron orbitals?
Question: Why does the uncertainty principle allow probing of characteristics specific to the electron orbital distribution? If you measure an electron's position/momentum, then after you measure ...
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2answers
167 views
Showing that position times momentum and energy times time have the same dimensions
I've been asked to show that both the position-momentum uncertainty principle and the energy-time uncertainty principle have the same units.
I've never see a question of this type, so am I allowed to ...
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1answer
481 views
Application of Heisenberg's uncertainty principle
I've the following application of Heisenberg's uncertainty principle.
If a beam of particles in localised in the $x$-direction by a long slit, what is the uncertainty in position?
Firstly, I ...
