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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87 views

Where this interpretation for the field modes comes from?

I'm reading the book "Modeling Black Hole Evaporation" by Alessandro Fabbri and Jose Navarro-Salas, and in section 3.3.2 they talk about wavepackets at $\mathscr{I}^+$. It all starts like this: one ...
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What does Hawking mean by “in empty space the field can’t be fixed at 0 because then it’d have both a precise value and a precise rate of change of 0”

Slightly modified the language in the title to make it fit in 150 characters. The above comes up in the part leading up to the explanation of how black holes emit particles.. My impression was that ...
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How to get the Number Phase Uncertainty relation from the Energy time relation?

I can arrive at $\Delta H\Delta t \geq \frac{\hbar}{2}$, but how do I get from there to $\Delta N\Delta \phi \geq 1$ for the number states of light? I know we write $H = \hbar \omega (N + \frac{1}{2})...
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momentum in calculation of Bohr's radius

Some usual calculations of the Bohr's radius (see 2.5 at Feynman's here, or this text here) starts by defining a radius $a$ ( most probable radius ? average radius ? ). Next, from Heisenberg's ...
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If the system is in an eigenstate of $B$, then $\Delta B = 0$, but $\frac{|[A,B]|^2}{ 4} \not = 0$, so how can uncertainty relation hold?

Let $A,B$ be two non commuting observables, then we do know that $\langle (\Delta A)^2 \rangle \cdot \langle (\Delta B)^2 \rangle \geq \frac{|[A,B]|^2}{ 4}.$ Also, we do know that, when the system ...
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1answer
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Heisenberg uncertainty principle meaning and using it to determine approximate sizes confusion

I was always under the impression that the Heisenberg uncertainty principle tells us to what precision we can make a momentum measurement given a position one. However, when doing quantum mechanics ...
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82 views

De Broglie Wavelength of a particle at the turning point of a fountain

If you think about an atom which is launched in some kind of straight fountain, upward in the gravitational field. At the turning point the velocity and therefore the momentum of the particle seems to ...
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Explanation of Different factor of $2$ in Formulas for the Uncertainty Principle [duplicate]

I am readind about Heisenberg's Uncertainty Principle and although the main formula most texts use is $$\Delta x\Delta p_{x}\geq \frac{\hbar}{2}$$ or equivalently $$\Delta x\Delta p_{x}\geq \frac{h}...
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35 views

Clarification on Heisenberg thought experiment

Heisenberg imagined a high energy photon was absorbed by an electron, but in order to make a measurement on that electron it will have to absorb another photon which means it velocity gets higher but ...
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1answer
121 views

minimum uncertainty in measurement of position

Suppose, I made a measurement of the position of an electron using a photon. How the minimum uncertainty in the measurement of the position be one wave length? Also how do we use waves to measure the ...
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How does Heisenberg's uncertainty work with more than one quantum field?

How does Heisenberg's uncertainty principle work with more than one quantum field? I am specifically asking about the time-energy uncertainty: $$\Delta E \Delta t \ge \frac {\hbar}{2}\tag{1}$$ Imagine ...
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If perfect blackness violates the Uncertainty Principle, how isn't dark matter a violation?

In a recent tweet, Dr. Michio Kaku stated that perfect blackness would violate the Heisenberg Uncertainty Principle, i.e. every object must emit some radiation. I have two questions regarding this ...
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635 views

How to get the radius of Bohr from the uncertainty principle?

I would like to know how to get the following result: \begin{eqnarray} a_0=\frac{4\pi\varepsilon_0 \hbar^2}{\mu e^2} \end{eqnarray} from the beginning of the uncertainty of heisenberg. If possible, I ...
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Are phase and particle (photon) number in QED conjugated variables?

I found in A. Zee's book "QFT in a nutshell" (1.edition) the interesting relation (8) respectively (9) in chapter III section 5 (p.173) which states that in a collective of non-relativistic bosons the ...
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1answer
88 views

What is 'definite' variable in QM?

I have gone through a few of the questions on the website regarding this particular query, but I have not understood what they meant. When a question says that a particle has definite momentum, are ...
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76 views

I have a thought experiment that defies the uncertainty principle - what's wrong with it?

There's a particle somewhere on the x-axis (this whole thing is 1-dimensional) at x0, which we do not yet know. I fire a photon at it from the origin with a known speed (c) and a known wavelength λ1 ...
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1answer
79 views

How can electron have known momentum?

In many exercises it is given that electron has a know speed, e.g. 5*10^3 m/s. But how is this possible when we deal with Heisenberg principle?
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Bond breaking stretch length with QM

In QM and assuming you could repeat the same exact bond-breaking experiment arbitrary number of times, do bonds always break at the same stretch length, or does the uncertainty principle require some ...
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Notation in Heisenberg Uncertainty Relation: greater than with tilde: $\gtrsim$

In "The Road to Reality" (pg. 523), Roger Penrose writes: Heisenberg's uncertainty relation tells us that the product of these spreads cannot be smaller than the order of Planck's constant, and ...
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1answer
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Would a neutron star-like celestial body made of bosons collapse because of missing Pauli repulsion?

Imagine the neutron star-like celestial body would be built up of bosons (assume that neutrons would be bosons). In that case there would be no Pauli repulsion (the exchange force of the exchange ...
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1answer
132 views

Is there an Heisenberg uncertainty relation for light polarisation?

While reading some questions about the polarisation of a photon, I was wondering about its quantum mechanical representation as a classical vector in the electromagnetic field operator : \begin{...
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1answer
47 views

Finding the uncertainty from a probability distribution?

If you have two properties, $A$ and $B$, that do not commute, and thus have a commutator $C$, and the uncertainties $\Delta A$ and $\Delta B$ obey the relation $$(\Delta A)(\Delta B)\geq \frac{1}{2}|C|...
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How to determine the approximate order of the strength of nuclear force from Heisenberg's Uncertainty Principle

Today I came across a question , where I was asked to find the Strength of nuclear force from Heisenberg's Uncertainty Principle... Please can anyone help me out... I have come across a solution ...
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Does diffraction change longitudinal component of k?

Say a monochromatic wave in 2D travelling in the $x$ direction passes an aperture of width $a$ at $x=0$. The amplitude distribution in $k_y$ afterwards will follow the Fourier transform of the shape ...
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2answers
80 views

Relation between momentum and momentum uncertainty

I have read the following sentence in a section which is explaining why particle accelerators need such high energy: As we require high precision position measurement, the Heisenberg uncertainty ...
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3answers
841 views

What is the meaning of natural line broadening?

I have recently found one exercise in an exercise book: During the transition from the first excited state of a hydrogen atom into the ground state, photons with a wavelength of 121.5 nm are ...
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Different statements of the Heisenberg's uncertainty principle [duplicate]

In different books, but also websites, there are different expressions for the Heisenberg's uncertainty principle. For example, $\Delta x \Delta p \ge h$ (from The Physics of Atoms and Quanta) $\...
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Zero uncertainity in components of angular momentum in Hydrogen atom

It is given that L and Lz,Lx,Ly commute.(L is total angular momentum, Lx is angular momentum along x axis). So, I can simultaneously know the value of let's say L and Lz. But, if I perform huge no of ...
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2answers
125 views

Heisenberg uncertainty principle

Is it true that an electron is fundamentally probabilistic in nature? That the Heisenberg uncertainty principle is not describing our limited ability to measure the particle's position and momentum ...
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2answers
127 views

Paragraph from a Stephen Hawking's Book (Uncertainty Principle)

This is from a Stephen Hawking's Book (Uncertainty Principle). I would like to know how does the Uncertainty Principle impose a limit on the size. What does he mean? From Hawking's book: It turns ...
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1answer
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Confinement energy of an electron in the nucleus

Hullo, I've got a relatively simple question in my homework and yet I can't seem to find a proper answer I need to find the confinement energy of an electron in a Deuterium nucleus with the radius ...
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1answer
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Is the uncertainty principle a circular argument? [closed]

Uncertainty is due to the measurement techniques humans tend to use requiring photoelectric effect. The Planck constant is due to the photoelectric effect. If the standard deviation of measurement was ...
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Uncertainty principle for a sitting person

If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths. What am I missing? Do ...
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4answers
250 views

QFT and vacuum energy [duplicate]

According to Quantum Field Theory, all 'particles' are oscillations in their own fields. And according to Vacuum Zero Point Energy and the Heisenberg Uncertainty Principle, these fields have ...
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Spread of the (smeared) field observable under time-evolution

Setup: Essentially, I'm interested in performing an analysis which is completely standard in QM, but I've never seen the analogue in QFT: Given I measure a system to have some value of its canonical ...
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3answers
842 views

Heisenberg energy uncertainty [duplicate]

I am biologist and just new to the field of quantum mechanics and trying to understand the subject by reading. It is said that virtual particles are created due to the uncertainty of energy when ...
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1answer
176 views

Uncertainty Principle - Accuracy or Precision? [closed]

While discussing about the Uncertainty Principle, some books use the word 'accuracy' and some other books use the word 'precision'. Some even use them both interchangeably. For instance, in Griffiths' ...
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Is information lost in the Heisenberg's uncertainty?

If I set a particle at a known momentum and a known position, then I would expect that I know the precise position and momentum upon measurement (assuming I can measure that well). The uncertainty ...
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1answer
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How can the derivation of the energy of an electron in a Fermi gas using the Heisenberg uncertainty principle be made rigorous?

When modeling a large number of non-interacting identical fermions in a potential well of volume $V$ as a harmonic oscillator and assuming the Pauli exclusion principle, it is easily seen that the ...
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1answer
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Is it possible to calculate the average value of $x^{2}p^{2}$ for an infinite square well? [duplicate]

If you can only measure either position and momentum in quantum mechanics how would one find the average value of $x^{2}p^{2}$ for an infinite square well?
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Uncertain principle mistake?

I believe I have a hole in my understanding of Heisenberg's Uncertainty Principle, but I'm not sure where it is. 1) Assume you have a source of monochromatic light, a laser, perhaps. 2) Assume it ...
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Heisenberg's uncertainty in nuclear physics

I'm doing a course in Nuclear Physics but I think it focuses more on the experimental side so not everything is that rigorous. In the notes, lecturer gives an argument for why we should use electrons ...
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1answer
159 views

Are there any ways to exclude uncertainty in the values of any non-commuting operators? [closed]

If two similar systems are created and In the first system the position is measured with accuracy and in the second one the momentum is measured with accuracy can this avoid the uncertainty in the ...
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1answer
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Why can't we partition the quantum-mechanical phase space into discrete cells?

Near the bottom of page 2 in this paper, von Neumann states that not only is it impossible to simultaneously measure $x$ and $p$, but also that it is impossible to partition the quantum-mechanical ...
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1answer
50 views

$u=(3/2)nRT$ when $T=0$

Why does a body with $0\ K$ temperate does the internal energy NOT become $0\ J$? My lecturer said it had to do with some quantum mechanics, but I never really got any answers from him. I really want ...
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65 views

Why does a narrower Gaussian wavepacket correspond to an increased $\Delta k$?

Please answer this question without too much reference to the Uncertainty Principle. I understand it in that respect. I'm just wondering in terms of Fourier analysis. Why does a more localized wave ...
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Are there wavefunctions that don't get more localized as we go backwards in time? [duplicate]

Gaussian wave packets spread as the time passes, which means that as we go backwards in time they get more localized. Therefore, Gaussian wave packets introduce less uncertainty in the position as the ...
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What's the speed of light when viewed from the side?

Suppose a pulse of light is sent from $A$ to $B$ in a rigid triangle $ABC$. While the pulse is moving from $A$ to $B$, what is it's velocity relative to $C$? The special character of the photon among ...
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1answer
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Meaning of units in the Heisenberg Uncertainty Principle

So we have the inequality $\Delta x\,\Delta p\geq \hbar/2$ Why is the uncertainty of position in meters? Isn't uncertainty measured in probabiliies? Does it make sense to say that the uncertainty in ...
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The uncertainty principle and probing small scales

The uncertainty principle states that $\Delta x\Delta p \geq \frac{\hbar}{2}$. So if you know momentum to high precision, you can't know position to high precision. In the context of accelerator ...

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