This tag is for Heisenberg quantum mechanical uncertainty principle.
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Heisenberg Uncertainty Principle scientific proof
Heisenberg's uncertainty principle states that: if the x-component of the momentum of a particle is measured with an uncertainty
$$\Delta \vec p_x$$
then its x-position cannot, at same time, be ...
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0answers
36 views
reference for wavepackets and uncertainty relation
Can someone suggest a reference for a rigorous proof(from harmonic analysis) that for any wavepacket other than the gaussian, we have an inequality ie \delta x \delta k > 1
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2answers
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Was uncertainty principle inferred by Fourier analysis?
I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
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Theoretical penetration limit for evanescent waves
Consider a problem in classical electrodynamics, when a monochromatic beam experiences total internal refraction when traveling from a medium with $n>1$ to a medium with refractive index $1$ - see ...
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2answers
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A thought experiment with Heisenberg's Uncertainty Principle [duplicate]
Possible Duplicate:
Could the Heisenberg Uncertainty Principle turn out to be false?
Thought Experiment
Ponder, for a moment, if I had a cube with 10cm sides which I'll name The Box. By ...
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1answer
284 views
Quantum uncertainty of particle falling in black hole
A stationary observer at infinity sees a particle of mass m falling in a supermassive Schwarzschild black hole. He observes an increasing redshift and sees the particle ceasing to progress when it ...
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2answers
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Conjugate Variables, Noether's Theorem and QM
What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
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1answer
112 views
What's the proper way to approximate the position uncertainty of a particle?
In this problem:
shouldn't $\Delta x\sim\lambda/\sin\theta$ be
$$\Delta x\sim \frac{\lambda}{\sin\theta} - \left(\frac{-\lambda}{\sin\theta}\right) = 2\frac{\lambda}{\sin\theta}$$
instead such ...
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3answers
306 views
An electron falling into a black hole
If an electron falls into a black hole. How can the Heisenberg uncertainty principle hold? The electron has fallen into the singularity now so it has a well defined position which means that it ...
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1answer
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Proof of quantum mechanical position uncertainty
How can you prove the uncertainty for position is:
$$\Delta{x} =\sqrt{\langle x^2\rangle-\langle x\rangle^2}$$
$\Delta{x}$, taken to be the root mean square of x.
$$\Delta{x} =\sqrt{\langle ...
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2answers
179 views
Measurement and uncertainty principle in QM
The Wikipedia says on the page for the uncertainty principle:
Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two ...
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3answers
394 views
Very simple example of the way the Fourier transform is used in quantum mechanics?
According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples ...
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Does uncertainty imply noncommutativity?
We already know that non-commutativity of observables leads to uncertainty in quantum mechanics cf. e.g. this and this Phys.SE post. What about the opposite: Does uncertainty imply noncommutativity?
...
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Will Determinism be ever possible?
What are the main problems that we need to solve to prove Laplace's determinism correct and overcome the Uncertainty principle?
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4answers
363 views
Uncertainty Principle for Information?
I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question:
While we have Heisenberg uncertainty principle on measuring coupled observables, ...
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3answers
150 views
Zero Point Fluctuations
The total energy of a mode in a quantum mechanical resonator is given by
$E_n ~=~ (n+ 1/2)hf$ where $n$ is the number of modes.
So when there are no modes or vibrations, i.e. $n=0$, the energy is ...
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0answers
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Naive Uncertainty principle for string theory
Is it possible, in some sense, that a naive uncertainly principle for string theory could be expressed as :
$$ \Delta x_i \Delta p_j \Delta \sigma ~=~ \delta_{ij} \hbar \ell_s$$
where $\ell_s$ is ...
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2answers
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Minimum possible Kinetic Energy of a confined electron
The problem is this:
Consider an electron confined in a region of nuclear
dimensions (about 5 fm). Find its minimum possible
kinetic energy in MeV. Treat this problem as
one-dimensional, and ...
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3answers
274 views
Energy-time uncertainty and pair creation
Usually, the energy-time analogue of the position-momentum uncertainty relation is quoted as $\Delta E \Delta t \geq \frac{h}{4 \pi}$. This has interpretational issues and such. But, with a suitable ...
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2answers
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Where does the “borrowed energy” come from in Alpha decay?
I was also thinking about the uncertainty principle in regards with energy & time. The question of something like:
Alpha tunneling out of the nucleus is where this can be invoked, but having an ...
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1answer
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wavefunction collapse and uncertainty principle
We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as ...
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3answers
284 views
Is it the act of measuring a quantum particle that causes it to lose its uncertainty?
I have designed an experiment. Without going into detail it resolves around the double slit quantum eraser experiments. If we can infer the location of a particle without actually measuring it, does ...
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2answers
346 views
The Heisenberg uncertainty principle: Interpreting $\Delta p$, $\Delta t$, etc
(1) I have a textbook question that states the following:
An electron has a speed of 500 m/s with an accuracy of 0.004%. Calculate the certainty with which we can locate the position of the ...
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4answers
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What is the meaning of uncertainty in Heisenberg's uncertainty principle?
The Heisenberg's uncertainty principle states the following:
$$\Delta p \cdot \Delta x \ge \frac{h}{4\pi}.$$
While studying for my high school physics exams, I fooled myself into believing that I ...
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2answers
316 views
Creation of particle anti-particle pairs
I was reading some QFT notes and there is one point that I don't understand, they are justifying why we need QFT saying that the number of particles is not preserved once we consider special ...
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2answers
345 views
Hamiltonian of oscillators quantized proof
https://docs.google.com/open?id=0BxrBcN1-BZWUOXNxR1l4S0l2MjQ
http://www.2shared.com/complete/Qjy1_uzp/Quantum_Mechanics_in_Simple_Ma.html
(I uploaded a pdf file that contains the parts of the ...
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3answers
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How does non-commutativity lead to uncertainty?
I read that the non-commutativity of the quantum operators leads to the uncertainty principle.
What I don't understand is how both things hang together. Is it that when you measure one thing first ...
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1answer
108 views
Quantum mechanics and Couder experiments
Couder experiments ( https://www.youtube.com/watch?feature=player_embedded&v=W9yWv5dqSKk and https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf), published in 2006, state that by dropping ...
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2answers
161 views
Why does $i ( LK-KL )$ represent a real quantity?
According to my textbook, it says that $i( LK-KL )$ represents a real quantity when $K$ and $L$ represent a real quantity. $K$ and $L$ are matrices. It says that this is because of basic rules. ...
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6answers
309 views
What would be likely to completely stop a subatomic particle assuming it was possible?
Suppose that completely stopping a subatomic particle, such as an electron, could happen under certain conditions. What would be likely ways to get an electron to be perfectly still, or even just stop ...
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4answers
771 views
Reason for the Gaussian wave packet spreading
I have recently read how the Gaussian wave packet spreads while propagating.
see:
http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics
Though I understand the ...
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1answer
197 views
Relativistic contraction for a wave packet and uncertainty on momentum
Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
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Could the Heisenberg Uncertainty Principle turn out to be false?
While investigating the EPR Paradox, it seems like only two options are given, when there could be a third that is not mentioned - Heisenberg's Uncertainty Principle being given up.
The setup is this ...
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1answer
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Does Heisenberg's energy-time uncertainty principle imply that quantum computing is no more efficient than classical computing?
See http://arxiv.org/abs/quant-ph/0006080v1 "On Non Efficiency of Quantum Computer", by Robert Alicki. In this paper, the author argues using Heisenberg's energy-time uncertainty principle, that ...
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1answer
133 views
uncertainty principle of spin in (super)string theory
In quantum mechanics, uncertainty principle states that we can only measure the quantity of spin in one axis but not others.
Then what about in superstring theory? As quantum mechanics is basically ...
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2answers
503 views
Why don't quantum effects invalidate the speed of light barrier?
While proving that no matter can reach the speed of light (a fact which I call the kinetic energy barrier), Einstein uses the fact that he can calculate the velocity and position of an electron. ...
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1answer
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How do you determine the degree of localization of a wavefunction?
Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
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Does the uncertainty principle apply to photons?
Wikipedia claims the following:
More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being ...
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0answers
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Non-simultaneous measurement of the location and momentum of an electron
I know the uncertainty principle tells us that we cannot simultaneously measure both the location and momentum of a particle with a high accuracy. The usual example we find in lectures is to imagine a ...
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1answer
254 views
Photons and uncertainty principle
Let's assume we have a perfect single-photon source: a device emitting exactly one photon at a time, with defined energy and direction. Let's shoot a photon: we know exactly the position of the photon ...
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1answer
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Determining the spin of wavefunction
We all know that by uncertainty principle, location of a wave-particle is perfectly determined when uncertainty of momentum becomes infinite. (I also heard that in reality, it is almost impossible to ...
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1answer
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Applying uncertainty principle and the difference in $\Delta x$
These two questions seem to be very similar, but the textbook uses a bit different methods for calculating $\Delta x$ of uncertainty principle.
Question A) Suppose that there is a room with the same ...
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1answer
294 views
Momentum in quantum mechanics
In quantum mechanics, we can have some superposition of matter waves that have different wavelengths. If then, can't momentum of a particle change every time measurement takes place? Or should I ...
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1answer
138 views
electrons in an atom and uncertainty principle
Electrons in an atom have quantized energy quantity. Can uncertainty principle be applied in this case, then?
How does this work?
As energy is fixed, this seems to disobey $\Delta E \Delta t \geq ...
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1answer
157 views
EPR paradox and uncertainty principle
In Wikipedia article EPR paradox,
The original paper purports to describe what must happen to "two systems I and II, which we permit to interact ...", and, after some time, "we suppose that there ...
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2answers
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Why is $\Delta x \Delta k \approx 1$ in any pulse?
In my physics textbook, it says that for any pulse, if $\Delta x$ becomes smaller, $\Delta k$ becomes larger where $k$ refers to $2\pi/\lambda$ and $x$ is x-axis displacement, as described by $\Delta ...
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3answers
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uncertainty of fields with many harmonic modes
In most basic level introduction to the quantum harmonic oscillator formulation of fields, it is assumed that the commuting variables for the fields $p_m$, $q_m$ are
$$ \lbrack p_m , q_n \rbrack = ...
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what is expectation values of this anti-commutator?
what is expectation values of this anti-commutator?
$$\langle \{ \Delta \hat x,\Delta \hat p\} \rangle$$
where the $\Delta \hat p=\hat p-\langle \hat p \rangle$ and $\hat p$ is momentum operator and ...
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4answers
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What is meant by “Nothing” in Physics/Quantum Mechanics(QM)?
I am not a phycisist, so please forgive my ignorance. This is related to my posts and this.
I am trying to undertand what is meant by the term "Nothing" in physics or Quantum Mechanics since it seems ...
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2answers
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Naive question on quantum mechanics and uncertainty principle
This is a follow up on this question, the answer of which points towards Quantum Mechanics.
As stated I am not a phycisist so please forgive my ignorance.
I will try to understand the issue by going ...
