This tag is for Heisenberg's quantum mechanical uncertainty principle. DO NOT USE THIS TAG for uncertainty in a non-quantum measurement.

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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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A quantum particle which is almost at rest but whose position is random!

Assume a particle is given by a quantum state which is constructed in such a way that it is equally probable to find it anywhere in an fixed interval $(0,L)$ but has arbitrarily low velocity. The ...
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Is it possible to determine timescales of electron dynamics from the natural linewidth of an electronic transition?

A lot of work has been done recently on electron dynamics using attosecond pump-probe techniques; for instance in this paper. In this particular paper, the authors photoionized the neutral ...
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Why isn't the Heisenberg uncertainty principle stated in terms of spacetime?

As I understand it, there are two "versions" of the Heisenberg uncertainty principle: Position-Momentum uncertainty \begin{equation} \sigma_x \sigma_p \geq \frac{\hbar}{2} \end{equation} where ...
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Rectangular window $\psi$ wave-function and the calculus of $\langle p^2\rangle$ for it

I'm currently considering a rectangular window $\psi$ function: $$ \psi(x) = \begin{cases}\left(2a\right)^{-1/2}&\text{for } |x|<a \\ 0&\text{otherwise.} \end{cases} $$ I am interested in ...
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Time-Energy Uncertainty Principle and Operators

In most of examples, I notice that uncertainty principle for time & energy is given between mass & lifetime. The UP for time and energy is $$ \Delta t\,\Delta E\geq\frac h{4π} $$ where $$Δt ...
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345 views

How do you measure a particle's postion or momentum?

This question is about the Uncertainty Principle $$\sigma_x \sigma_p ~\ge ~\frac{\hbar}{2}.$$ Looking at the maths, I understant why the uncertainty in the poistion increases as the uncertainty in ...
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Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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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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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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Is the number-phase uncertainty relation classical?

For a harmonic oscillator in one dimension, there is an uncertainty relation between the number of quanta $n$ and the phase of the oscillation $\phi$. There are all kinds of technical complications ...
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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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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 ...
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Why $\Delta x \Delta p_x$ for stationary states increase linearly with n?

Harmonic Oscillator $\displaystyle \Delta x\Delta p_x = \hbar (n+\frac{1}{2})$ Particle in a box $\displaystyle \Delta x\Delta p_x = \frac{\hbar}{2} \sqrt{(\frac{n^2\pi^2}{3}-2)}$ We notice ...
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Integral equations contradict The Uncertainty Principle?

I was reading about Integral equations, and I found this excerpt in Portuguese Wikipedia: "integral equations serve to determine the position in all instances of an object, if known, its ...
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471 views

An electron in $s$ state

If an electron is in $s$ state, for example in 1s state for Hydrogen or 5s state for Silver atom, $\ell=0$. So,its total angular momentum $L$ is also equal to 0. So, what is electron actually doing in ...
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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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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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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: ...
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QFT and violation of Heisenberg uncertainty principle

In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time: $$\Delta t<\dfrac{\hbar}{2\Delta E}$$ ...
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Two explanations of non-zero atomic radius

I have came across two separate explanations for why atoms have a positive atomic radius (as opposed to electrons "collapsing" into the nucleus). The first is via Heisenberg Uncertainty Principle, ...
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Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
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Two questions about Feynman propagator

Taking for example the meson propagator: $$ \Delta_F (x-y) = \int \frac{d^4k}{(2\pi)^4} \frac{e^{-ik(x-y)}}{k^2 - m^2 + i\epsilon}. $$ It describes a meson that propagate from a point of Minkowski ...
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Is single photon perfectly monochromatic?

Now, we do have equipment to generate single photon at a time, and LASERs are nearly monochromatic. While typing the question, am realizing that successive photons in case of single photon ...
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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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Rigorous Mathematical Proof of the Uncertainty Principle from First Principles

While looking at an intuitive explanation for the Heisenberg Uncertainty Principle (related question below), there was a mention of an axiomatic approach to establishing the uncertainty principle. ...
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Do the position-momentum uncertainty and time-energy uncertainty really exist in QFT?

It is well known from the Quantum Mechanics(QM) that for a particle, there is a position-momentum uncertainty relation: $$\Delta x\cdot \Delta p\geq \frac{1}{2}\hbar,$$ which bascically can be derived ...
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344 views

Why do we need virtual particles?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
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Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question. The ...
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369 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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667 views

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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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 ($k$ ...
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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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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 ...
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Minimum Uncertainty Wavefunction derivation

Can anyone point me to a reference (preferably either something online or something a small liberal arts school would be likely to have in its library) that goes through a derivation of the minimum ...
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Holding an electron

Heisenberg has said that the position and velocity of a small object cannot be known 100% accurate. Now, suppose I take a big metal box within which there is only one electron (somehow). I don't know ...
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Is the Uncertainty Principle a logical consequence from the Wave-Particle duality?

I always thought of the Uncertainty Principle as a logical consequence that follows from the Wave-Particle duality, or more precise, from the fact that all particles behave as waves as long as they do ...
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Does there exist a state for which $\Delta\sigma_x^2=\Delta\sigma_y^2=0$? If not, how does one prove it?

I just realized that the uncertainty principle says that $$\Delta\sigma_x^2 \Delta\sigma_y^2 \ge \left(\overline{\hat\sigma_z}\right)^2,$$ where ...
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The Physical Meaning behind a Commutator [duplicate]

I've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of ...
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electron orbits

Is there an upper limit to the number of orbits an electron can have around say a proton? Arent there states that are unstable(for n!=1) with corresponding mean/half lives and therefore uncertainty in ...
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'The size of an atom' using Uncertainty Principle

Suppose we have a hydrogen atom, and measure the position of the electron; we must not be able to predict exactly where the electron will be, or the momentum spread will then turn out to be ...
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“Derivation” of the Heisenberg Uncertainty Principle

The question I outline below is my textbook's "derivation" of the Heisenberg Uncertainty Principle. The "derivation" my textbook uses involves wave packets. Suppose there are seven waves of ...
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The Uncertainty Principle and Energy Nonconservation

The uncertainty principle is listed in most textbooks and articles as $$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$ This can be derived in many ways in many different settings, most of them involving ...
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Estimating minimum energy with uncertainty principle

I'm currently trying to solve a problem that involves estimating the minimum energy of a particle in the potential: $$ V(x) = \frac{-V_0a}{|{x}|} $$ I'm quite confused about how to handle the ...
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208 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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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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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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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 ...
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Heisenberg uncertainty in Bose Einstein condensate

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 ...
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Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...