This tag is for Heisenberg quantum mechanical uncertainty principle.

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What physical significance has the Heisenberg Group?

I read that the canonical commutation relation between momentum and position can be seen as the Lie Algebra of the Heisenberg group. While I get why the commutation relations of momentum and momentum, ...
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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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107 views

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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513 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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716 views

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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66 views

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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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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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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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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202 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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Introductory derivations of Heisenberg uncertainty principle

I'm not an expert when it comes to quantum mechanics, so correct me wherever I'm wrong, but: I've always been a little bit bothered by introductory derivations of the Heisenberg uncertainty relations ...
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“Derivation” of the Heisenberg Uncertainty Principle

Ok, so I posted this in the mathematics StackExchange, but got no response. The question I outline below is my textbook's "derivation" of the Heisenberg Uncertainty Principle. The "derivation" my ...
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132 views

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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760 views

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 ...
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919 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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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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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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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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363 views

3D Minimum uncertainty wavepackets

Based on the 1D case mentioned in Griffiths, I decided to try looking at the features of 3D Gaussian wavefunctions, i.e. (position basis) wavefunctions of the form $\psi(\mathbf{r}) = ...
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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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932 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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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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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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697 views

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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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 ...
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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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461 views

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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Calculating de Broglie wavelength

Hey, trying to finish an assignment but having some trouble with it. I will show all my work. The topic is on wave/particle dualty, uncertainty principle (second year modern physics course). So the ...
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Does measuring the exact position of a ball destroy the ball

If you have a macroscopic ball (say, a tennis ball) and you (hypothetically) try to measure the exact position of the center of that ball by measuring the exact positions of the atoms making up the ...
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337 views

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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Question on the uncertainty principle

The problem statement: Measurement detects a position of a proton with accuracy of $\pm10pm$. How much is the position uncertainty $1s$ later? Assume the speed of a proton $v\ll c$. What i ...
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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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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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640 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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First-order and second-order wave equations, versus the uncertainty principle

In classical physics, we have second-order equations like Newton's laws, so we need to specify both position (zeroth order) and velocity (first order) of a particle as initial conditions, in order to ...
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1answer
185 views

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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Uncertainty on a single observable measurement

Heisenberg Uncertainty Principle states (in the form of the Robertson-Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement ...
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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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528 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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685 views

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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Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes ...
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Why the uncertainty principle can be used for estimation?

It is usually said/done in textbooks and classes that if $\Delta x$ is known then $\Delta p_x$ can be estimated using the uncertainty principle as $\Delta p_x \sim \hbar/\Delta x$. But the ...
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422 views

Why is classical physics not valid for a harmonic oscillator in its lowest energy state? [closed]

I am reading Born's interpretation of wave function in quantum physics by Eisberg & Resnick and I am not able to understand this description about comparison between the classical and quantum ...
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1answer
92 views

Does Heisenberg uncertainty apply within each quantum configuration, or in the amplitude distribution over them?

I'm still absorbing some basic ideas about quantum physics and now I think I have to reconsider the Uncertainty Principle. Here is what I understand, in summary: a "configuration" specifies the ...
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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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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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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) ...