This tag is for Heisenberg quantum mechanical uncertainty principle.

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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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3answers
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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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953 views

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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4answers
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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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2answers
515 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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1answer
111 views

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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2answers
264 views

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
205 views

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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1answer
1k views

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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1answer
389 views

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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655 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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3answers
629 views

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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1answer
314 views

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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4answers
708 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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2answers
747 views

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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1answer
418 views

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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759 views

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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1answer
225 views

Uncertainly Principle in orthogonal directions

The Heisenberg Principle states that for each direction, $\Delta x\cdot \Delta p_x \ge \hbar , \Delta y\cdot \Delta p_y \ge \hbar$ and $\Delta z\cdot \Delta p_z \ge \hbar$. But, can anything be said ...
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Does the HUP alone ensure the randomness in QT?

This answer of mine has been strongly criticized on the ground that it is no more than a philosophical blabbering. Well, it may well be. But people seem to be of the opinion that HUP alone does not ...
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Does Heisenberg's uncertainty under time evolution always grow?

Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting ...
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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 ...
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1answer
311 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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1answer
564 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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343 views

Would something like the uncertainty principle arise even if the universe was built on something like Newtonian mechanics?

I am thinking of a (greatly simplified) computer simulation of a universe that followed something like Newtonian rules. Inside the simulation are A.I.s that are made from those same rules, and can ...
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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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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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1answer
210 views

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 ...