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Questions tagged [heisenberg-uncertainty-principle]

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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4
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2answers
91 views

Will a “big rip” scenario cause an “absolute zero universe”?

To my best understanding, in a "big rip" scenario the universe expands faster and faster, until it expands between particles faster than the particles can hold one another. Does that mean that at ...
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2answers
112 views

Does the Uncertainty Principle imply a linear cosmology?

If the uncertainty in the age of the Universe is $\Delta t$ then the Uncertainty Principle implies that it has an uncertainty in its energy $\Delta E$ given by $$\Delta E \ \Delta t \sim h.\tag{1}$$ ...
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1answer
41 views

Is it possible to measure the momentum components at same time in QM?

It is well known that the components of momentum in quantum mechanichs commute, like this $$ [P_x,P_y] = 0 $$ Basically, it means that the momentum components can be measured independently. Since ...
-1
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2answers
80 views

Is energy always uncertain? [duplicate]

ΔE⋅Δt⩾ℏ/2 Does the energy time uncertainty principle imply that an object would have to stay for an infinite amount of time in a state for there to be no uncertainty in the energy of that state?
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2answers
67 views

Is it theoretically possible to control or modify the probability of finding an electron?

We know that according to Quantum physics , electrons are not just regular particles with discrete location, and they kind of occupy all the space which has the ‘ highest probability ‘. We can also ...
2
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0answers
131 views

Why is information conservation not restricted by the uncertainty principle?

The idea of information conservation seems to be: if all field equations/states of all particles/matter/waves at a certain time are known, all trajectories/waves can be backpropagated to retrieve all ...
1
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2answers
660 views

why path of an electron in an orbit is uncertain?

I have read the quantum mechanical model of an atom which says that path of an electron around the nucleus is uncertain due to uncertainity principle which says that it is impossible to measure both ...
0
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1answer
83 views

Heisenberg's uncertainty principle and measurements

While studying quantum key distribution, I came across this postulate which states that given two entangled particles A and B at Alice and Bob sites respectively, if Alice measures A to be $\uparrow$ ...
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0answers
51 views

Heisenberg uncertainty in $L^2([0, 1])$ space [duplicate]

I'm given a system represented by a Hilbert space $L^2([0, 1])$. In this space, the momentum basis is $\frac{1}{\sqrt{L}} \exp{\frac{2 \pi i nx}{L}}$. It seems like Heisenberg uncertainty would be ...
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1answer
68 views

Quantum Physics - Definite Energy/Momentum

I'm new to this site and I would like some help about a tiny matter. We know that the Heisenberg Uncertainty Principle can be either focused on the Displacement/Momentum formula and the Energy/Time ...
0
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1answer
134 views

Smallest uncertainty ever achieved in position measurement in QM?

The Heisenberg uncertainty principle states that $$\Delta x\Delta y\geq\hbar/2$$ Since the magnitude of $\hbar$ is $10^{-34}$ we could measure both $x$ and $p$ with an uncertainty magnitude of $10^{-...
2
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1answer
173 views

Heisenberg's uncertainty principle for MRI

In the nuclear magnetic resonance imaging (MRI), the spatial resolution and temporal resolution can not be arbitrarily reduce simultaneously. What would be a simple inequality of the Heisenberg's ...
-3
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1answer
149 views

Which experiment clearly shows us that Heisenberg Uncertainty Principle is ontological and not epistemological?

I have heard that the Heisenberg Uncertainty Principle(HUP) is not because of our limitations in measuring and the apparatus used but instead because of the very way things are I searched online in ...
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0answers
46 views

What's the invariance quantity under EPR and Bell's inequality?

I was reading and writing a study report about EPR and Bell's inequality. As the hidden variable and local realism was proven to be "false", and from many posts in physics exchange websites such as ...
2
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2answers
273 views

Is momentum perfectly conserved at the particle level given the Heisenberg uncertainty principle?

Discussions of conservation of momentum frequently use the metaphor of two billiard balls colliding. My impression is that this is not valid at the quantum scale - an illustration of the particles' ...
1
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1answer
261 views

Uncertainty of angular momentum

Is it correct to write for the uncertainty $$\Delta \vec L=\Delta L_x+\Delta L_y+\Delta L_z$$ meaning $L$ is the angular momentum and $L_x,L_y,L_z$ the components. I couldn't find an answer in my ...
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1answer
251 views

Question on Uncertainty Principle in a Potential Well

The following is the problem that I'm struggling with from the book of Gasiorowicz: If we have an electron in a potential well of width $a$ and depth $V_0$, then the kinetic energy is, by the ...
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0answers
51 views

Niels Bohr's Calculation of Einstein's Photon Clock Thought Experiment

I was reading a book and there was written that Einstein came up with the Photon Clock thought experiment to prove Heisenberg's Uncertainty principle wrong. But, Niels Bohr proved (by calculation) ...
1
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1answer
263 views

On the Robertson uncertainty relation when $\big|\dfrac{1}{2} \langle\{A,B\}\rangle - \langle A \rangle \langle B \rangle \big|^2 \neq 0$

The Robertson uncertainty relation is $\sigma^2_A \sigma^2_B \geq \big|\dfrac{1}{2} \langle\{A,B\}\rangle - \langle A \rangle \langle B \rangle \big|^2 + \big| \dfrac{1}{2i} \langle [A,B] \rangle \...
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0answers
77 views

What does zero in zero point energy refers to?

I know due to Heisenberg uncertainty principle even empty space can have lots of particles constantly popping in and out of existence, this also means that absolute zero cannot exist but what does ...
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1answer
67 views

How precisely can position and energy be measured simultaneously?

What will be the equation of measuring energy $E$ and position $x$ in terms of $x$, $m$, $\omega$, $p$, and fundamental constants?
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2answers
317 views

Single slit experiment and the uncertainty principle - contradiction?

I have read for example here that the single slit experiment can be seen as a visualisation(?) of Heisenberg's Uncertainty principle. Basically, the photons passing through the slit are given a fixed ...
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0answers
34 views

QCD Conjugate Variable Determination

This is not homework question. I have not been in school for over 40 years. Are there conjugate variables in QCD? How are they determined? I can relate to Heisenberg uncertainty in QM as the ...
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1answer
95 views

Uncertainty product at $t=0$ for a constant equation

Given the S.E $$ \Psi(x,0) = \begin{cases} A,&0 \leq x \leq \frac{a}{2}, \\ 0,& \rm elsewhere \end{cases} $$ I'm supposed to find the uncertainty product at $t=0$. However since the equation ...
0
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1answer
108 views

Uncertainty relation in mixed states

If a system is in a pure state $|\psi\rangle\langle\psi|$ we have $$\sigma_A\sigma_B\geq\frac{1}{2}|\langle[A,B]\rangle|.$$ Generalize this and find an uncertainty relation for an arbitrary mixed ...
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1answer
54 views

On the uncertainty relation of Heisenberg

in the uncertainty relation of Heisenberg ΔxΔp≥ℏ/2 (1) why we do not take the minus sign of ℏ/2? i know from the derivation of this relation that we take the square root in the end so it is should ...
2
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1answer
317 views

Why do position operators in orthogonal directions commute?

In three dimensions, we have $\hat x$, $\hat y$, $\hat z$ as the position operators in the three orthogonal directions. If the components of angular momentum don't commute, why must these all commute? ...
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3answers
163 views

What does self-closing bra-ket mean in Robetson-Schrodinger Uncertainty Relation?

I was reading: https://en.wikipedia.org/wiki/Heisenberg%27s_uncertainty_principle#Robertson–Schrödinger_uncertainty_relations Where an inequality is presented: $$ \sigma_A \sigma_B = | \frac{1}{2} \...
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1answer
492 views

Quantum Tunneling, Superposition, and The Uncertainty Principle

After looking through various papers and articles on explanations of quantum tunneling I've been left wondering about one thing. I've read explanations of tunneling as an affect of a particles wave ...
3
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1answer
259 views

Time-Energy Uncertainty Relation when $A$ depends explicitly on $t$

There are several questions asking by the meaning of Time-Energy uncertainly relation and also by its derivation. My problem is about the second. In all documents I have seen, the same is supposed ...
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0answers
249 views

State of minimum uncertainty of a particle in an infinite square well

Let $\sigma_x$ and $\sigma_p$ be the standard deviation of position and momentum of a particle. The ordinary uncertainty relation tells us that in general we have $$\sigma_x\,\sigma_p\geq\hbar/2.$$ ...
2
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2answers
55 views

Would we be able to be consistent in our theory if we were to only assume the particle nature of matter with the uncertainty principle

As far as I understood, the uncertainty principle is direct consequence of the wave - particle duality of matter; however, would we be able to be consistent in our theory if we were to only assume the ...
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2answers
62 views

Uncertainty Principle for Compound Objects Interpretation

The most common misstatement of the HUP seems to be that it's a constraint on knowledge of a system or particle, rather than a description of the behavior of the system itself. E.g. an electron is ...
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2answers
109 views

Confusion about uncertainty principle

A book is lying on the table. It is at rest. Its velocity is 0 and uncertainty in velocity $\Delta v$ is 0. Does this mean that uncertainty in its position is ∞?
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2answers
314 views

Particle in a box momentum and position, expectation and uncertainty in stationary states

For stationary states solution for a particle in a box in infinite wall. i.e. $\psi=Ax(a-x)$ for $x\in[0,a]$. $<x>=L/2$ would be a definite solution. Similarly, $<p>=0$, where $<p^2>...
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1answer
52 views

How big will the wave packet be?

I want to find out how big a Gaussian wave packet of a $C_{60}$ beam of 300 m/s is after 100 ms of propagation if the initial $1/e^2$ confinement was 12 pm? I know for a Gaussian wave packet the ...
1
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2answers
268 views

Is the Uncertainty Principle and the Observer effect the same thing?

I've read the relevant Wikipedia entries, Why shouldn't the uncertainty principle be interpreted as an observer effect? and What is the uncertainty principle? There are a lot of equations and ...
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2answers
223 views

Is it fair to say that signal processing is a quantum phenomenon?

I recently saw a video by 3Blue1Brown, in which he explained that the uncertainty principle isn't a quantum phenomenon, but a result of basic signal properties. The basic premise was: the more precise ...
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1answer
104 views

What is the spreading for rectangular wave packets?

I know the spatial width for rectangular wave packets, but what is the spreading for a rectangular wave packet?
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1answer
556 views

Simultaneous measurement of two observables

In quantum physics the configuration of a particle is fully defined by it's wave function. When a measurement of a particular observable ( eg. position, angular momentum etc.) is made on the particle ,...
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0answers
107 views

Is the Heisenberg uncertainty principle based on experimental imprecision in measurement? [duplicate]

As far as I understand, the Heisenberg uncertainty principle states that the more one of the conjugate quantities are known, the less the other is known. So for instance, if the velocity of a particle ...
0
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1answer
66 views

Energy differences and matrix mechanics

I was reading a wonderful explanation of matrix mechanics on mathpages1. There we see that $\hat{q}_{mn}=q_{mn}\exp(i(E_m-E_n)t/\hbar )$ and consequently using Hamilton's classical equations we arrive ...
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1answer
140 views

How can the Heisenberg uncertainty inequality be defined in the unordered complex field $\mathbb{C}$?

The generalized uncertainty principle says, $$\sigma_A^2\sigma_B^2~ \ge ~\frac14\langle i[A, B]\rangle^2.$$ But the complex field is not ordered, i.e, inequalities like $\le$, $\ge$, etc are absurd. ...
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1answer
120 views

In the case of the time-independent Schrödinger equation, what is the uncertainty on the measurement of the energy of the particle?

Because there only exist stationary state solutions of the time-independent Schrödinger equation, which correspond to states with single, definite energies, and the energy expectation value is equal ...
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1answer
75 views

Statistical Mechanics

When I was reading statistical Mechanics it has written "by using phase space , the 6N(3N coordinate axes and 3N momentum axes) coordinates can represent the position and momentum of all the molecules ...
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0answers
71 views

Heisenberg's original Quantum Condition

In Heisenberg's paper Quantum Theoretical Re-interpretation of Kinematic and Mechanical Relations where he first derives Quantum Mechanics, using his postulates of Quantum Mechanics and the Old ...
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1answer
56 views

Potentials and position uncertainty

In the Schrodinger equation, we have some potential $V(x)$. But generally, there is some uncertainty in the position with solutions to Schrodinger's equation. Classically, we would say that a particle ...
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0answers
133 views

Natural line width for doubly excited transitions

So a simple derivation for natural single electron emission line broadening is this: $\Delta E \Delta t \approx \frac{h}{2\pi} \Leftrightarrow h\cdot\Delta f_{1/2}\cdot\tau \approx \frac{h}{2\pi} \...
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3answers
95 views

Uncertainty principle on optical fiber communication

While the calculations seem fine, I can't make sense of the solution to this problem. How can the uncertainty principle be used to tell us what the shortest pulse is? Wouldn't using it tell us the ...
5
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1answer
405 views

How did Heisenberg come up with the Canonical Commutation relation ($\hat X \hat P-\hat P\hat X=i\hbar$)?

All answers to questions like this dodge the question by saying it's a postulate of Matrix Mechanics, so let me rephrase it. Instead of how to derive the CCR, how does it follow from Heisenberg's ...