This tag is for Heisenberg quantum mechanical uncertainty principle.

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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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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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201 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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456 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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609 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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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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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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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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594 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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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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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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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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363 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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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
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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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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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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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265 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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1answer
556 views

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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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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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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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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485 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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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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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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458 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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274 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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293 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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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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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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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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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 ...
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problem with the last terms of uncertainty principle

i've problem with the last terms of uncertainty principle: 1. are these equalities true: $$\langle \{\Delta \hat A,\Delta \hat B\} \rangle=\langle \{\hat A, \hat B \}\rangle$$ $$\langle [\Delta \hat ...
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is there any uncertainty on the free particle with a definite momentum $\vec p$?

The probability amplitude for a free particle with momentum $\ p$ and energy $E$ is the complex wave function: $$\psi_{(\vec x , t)}=e^{i(\vec k\cdot \vec x -\omega t)}$$ is there any uncertainty on ...
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1answer
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Will photon's energy be exactly same after million years?

If photon will travel for million years without collisions, what subtle effects can be accumulated ? Gravity fields affect trajectory, but is energy completely intact after fly by ? Photon has its ...
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How does position uncertainty change in time?

I have an online homework for my Modern Physics class, that requires me to find the uncertainty in velocity and position of a duck. The question is as below: Suppose a duck lives in a universe in ...
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Uncertainty principle in infinite potential well

Consider infinite potential well i.e. Hilbert space $L^2 \bigl([0,1]\bigr)$. Next we consider subset $$D_\theta = \left\{ \psi \in L^2 \bigl([0,1]\bigr) | \; \psi \; \text{is absolutely continuos and ...
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Generalizing Heisenberg Uncertainty Priniciple

Writing the relationship between canonical momenta $\pi _i$ and canonical coordinates $x_i$ $$\pi _i =\text{ }\frac{\partial \mathcal{L}}{\partial \left(\frac{\partial x_i}{\partial t}\right)}$$ ...
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Concept of a point particle in quantum mechanics

A point particle is usually thought of as structureless and without dimension. However, given that Heisenberg's uncertainty principle prohibits us from knowing the position of a particle exactly, what ...
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816 views

Operators Uncertainty

$\hat A$ is an operator. The uncertainty on $\hat{A}$, $\Delta A$ is defined by: $$\Delta A=\sqrt{\langle\hat A^2\rangle - \langle\hat A\rangle^2}$$ what is difference between $\langle\hat ...
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Why can't we know the speed, $\vec{v}(t)$, and position, $\vec{r}(t)$, of an electron (the two) at the same time $t$?

I've read something about this and I conclude that it happens because of the uncertainty principle. But I don't understand very well the meaning of that. I mean, it's very abstract that the speed, ...
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Heisenberg's principle in Quantum Cryptography

In quantum cryptography why do we need the Heisenberg uncertainty principle? Edit: I only know the statement of the Heisenberg uncertainity principle. As I know that if Eve tries to know the ...
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766 views

Uncertainty Principle for a Totally Localized Particle

If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, ...
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Who first realized the uncertainty principle allows for virtual particle pair production?

For all I've read about Quantum Field Theory I've never seen the concept of the living vacuum accredited to someone in particular. Given the importance of this very application of the uncertainty ...
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Do stationary states with higher energy necessarily have higher position-momentum uncertainty?

For simple potentials like square wells and harmonic oscillators, one can explicitly calculate the product $\Delta x \Delta p$ for stationary states. When you do this, it turns out that higher energy ...
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Noether's theorem vs. Heisenberg uncertainty principle

In continuation of another question about Noether's theorem I wonder whether there exists some kind of relationship between this theorem and the Heisenberg uncertainty principle. Because both the ...
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The complementary variable to the qubit and spin-1/2

The qubit is a big topic of quantum information theory. A qubit is a single quantum bit. Physical examples of qubits include the spin-1/2 of an electron, for example, see page 39 of Preskill: ...