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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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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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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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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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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Heisenberg uncertainty principle

In the double slit experiment, an electron interferes with itself and creates the pattern because it is in a superposition, traveling through both slits. If we place a detector at one slit, the wave ...
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Heisenberg Uncertainty Relation and Relativity

It's well known that in QM the position and momentum of a particle cannot be known simultaneously. It's also well known that in special relativity the idea of simultaneity loses its meaning. Would it ...
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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 $\Delta\sigma_x^2=\overline{(\hat\sigma_x-\overline{\...
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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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Why doesn't $σ_xσ_p$ change with the width of the well in the infinite square well problem (intuition)?

I calculated that the product of the uncertainty in position $\sigma_x$ for the ground state of an infinite square well of width $L$ with the uncertainty in the momentum $\sigma_p$ for the same state, ...
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Is quantum physics truly random or does it just appear that way because of Heisenberg uncertainty principle

The behavior of an electron (and other tiny things) is said to be probabilistic because we can't say where an election will be when we measure it, but only where it will probably be. As I understand ...
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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 infinite. ...
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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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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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Gaussian Minimizes Uncertainty - Statement Qualification [duplicate]

On the last page of this paper, the following statements are made (I'll jump right to around the point of interest): Example: Consider $A=p_x$, $B=x$. Then $$\langle A\rangle=\langle B\...
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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 ...
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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 ...
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Quantum mechanics,and how the law $ΔxΔp≥ℏ/2$ explains the paradox regarding atoms [duplicate]

In Chapter 2-3,Vol I of the Feynman lectures, Feynman talks about a rule in quantum mechanics that says that one cannot know both where something is and how fast it is moving. That the uncertainty of ...
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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 ...
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Are “uncertainties” in Heisenberg Uncertainity just standard deviations? [closed]

Can someone confirm that the uncertainties in Heisenberg's uncertainty relation are really just standard deviations based on the expectation values? For example, the $\Delta x$ can be computed by $\...
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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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Causality and Quantum uncertainty [duplicate]

Possible Duplicates: Why quantum entanglement is considered to be active link between particles? Why can't the outcome of a QM measurement be calculated a-priori? Why do some (the majority of?)...
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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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Does the uncertainty principle imply the existence of particles that exceed the speed of light?

The uncertainty principle allows for the creation of virtual particles (with non-zero mass) that exist for very short durations. This allows empty space to have particle pairs that pop into existence ...
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Which way will the pencil fall?

Let's say you had a perfect pencil, with a point which was just that one point (see this question). The pencil's mass was perfectly distributed, and there are no flaws in the craftsmanship. Let's say ...
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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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Spectral Line Width and Uncertainty principle

so I've been at this for about 3 - 4 hours now. It is an homework assignment (well part of a question which i've already completed). We did not learn this in class. All work is shown below. An ...
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How do I get observables to calculate uncertainty?

Given an infinite potential square well with $0<x<L$, I need to calculate the uncertainties of position and momentum. The eigenstates in the position basis are $$\lvert E_n\rangle\to \psi_n(x)=\...
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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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Is the wavelet transform utilized at all in QM?

Excuse any ignorance, but something was on my mind today and my professor didn't give me a very clear answer... Obviously the Fourier Transform is used pretty constantly in QM. What about the wavelet ...
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Uncertainty principle

Think of a particle known to be trapped in a box of size $\Delta x$ and cooled down to near absolute zero. I know that attempting to measure the momentum of this particle repeatedly will give a random ...
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Why doesn't gravity act as a measurement?

I think this must be a very basic question but I couldn't find the answers anywhere. I was starting reading about Quantum Mechanics and these questions came in mind: As I understand the quantum ...
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Uncertainty principle and multiple observers

My understanding is that an observer can measure the precise location of a particle so long as the corresponding uncertainty in momentum measurement is not an issue and vice-versa. Say there 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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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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Why is Heisenberg uncertainty principle not valid in waves in string?

We know from high school physics that when the incident wave is traveling from a low density region (high wave speed) region towards a high density (low wave speed) region on a string, the width of ...
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Measuring position and momentum at the same time?

In a non-relativistic quantum mechanical system in an infinite potential well. I try to measure the energy and the position of the system simultaneously. Since, the respective operators do commute ...
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Is it only the ground state of the quantum harmonic oscillator that has the minimum uncertainty product?

We know that the uncertainty product of general states is bounded by the inequality described by Heisenberg's uncertainty relation. And the ground state of the quantum harmonic oscillator falls under ...
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Theoretical Upper Bound on Processor Speed?

Barring aside considerations such as heat dissipation, capacitance, etc... (aka any sort of technological issue) what is the fastest speed of a processor? I am told that at distances of 1 planck ...
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Physical meaning of uncertainty principle + question on symmetry

A question on the Uncertainty principle. So we know that it says (for position and momentum) that: $$ \Delta x \Delta p \ge \hbar/2 $$. Where $\Delta p = \sqrt {<p^2> - <p>^2 }$ and $\...
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Quantum uncertainty in cell functions

In class today (philosophy of the mind) we discussed the ideas of Richard Lewontin. He stated that in determining the phenotype of a gene we must take into account the environment but also quantum ...