This tag is for Heisenberg quantum mechanical uncertainty principle.

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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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Quantum entanglement, quantum measurement, spin and position

By uncertainty principle, we know that determining particle's position at some location is limited. So we cannot determine the position of a particle at some exact point location as this would make ...
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What constitutes an observation/measurement in QM?

Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle. What is the technical definition of an observation/measurement? If I look at a QM system, it ...
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Physical Significance of Fourier Transform and Uncertainty Relationships

What is the physical significance of a fourier transform? I am interested in knowing exactly how it works when crossing over from momentum space to co ordinate space and also how we arrive at the ...
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Uncertainty relation and Energy-Position interference

How would you prove that the simultaneous measurements of position and energy are not subject to interference? I was thinking in calculate the commutation relation between $x$ and $H$ (Because $\Delta ...
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Semiconductors and localization of the electrons

When looking at the band diagram of a semi-conductor, direct conclusion of the invariance under discrete translations, for a filled state with an electron, one does know precisely it's momentum, so my ...
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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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How does QM allow imaging of individual electron orbitals?

Question: Why does the uncertainty principle allow probing of characteristics specific to the electron orbital distribution? If you measure an electron's position/momentum, then after you measure ...
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Showing that position times momentum and energy times time have the same dimensions

I've been asked to show that both the position-momentum uncertainty principle and the energy-time uncertainty principle have the same units. I've never see a question of this type, so am I allowed to ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...