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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How the electron delocalization can lower its kinetic energy?
In covalent bonding, as in metallic bonding, the lowering in energy relative to the free-atom state is achieved by the reduction in the kinetic energy of valence electrons due to their delocalization.
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Using the uncertainty principle to estimate energies in ground states
Suppose, for example, that we want to find the minimum energy of a particle undergoing simple harmonic motion. In classical mechanics, the energy is:
$$E = \frac{p^2_x}{2m} + \frac{1}{2} m \omega_0^2x^...
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What is the meaning of uncertainty principle in the case of hidden-variable theories?
What would be the meaning of the uncertainty principle in the case of hidden-variable interpretations of quantum mechanics, especially contextual hidden-variable theories?
Edit: Another way to put ...
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Derivation Heisenberg Uncertainty
I know there have been many questions posted regarding the derivation of the Heisenberg Uncertainty. I do not want to derive its general form, but instead I would like to calculate its lower minimum ...
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The Mathematic Tricks in the Derivation of Heisenberg Uncertainty Principle
I'm studying the derivation of Heisenberg Uncertainty principle but stuck with the mathematic trick.
When deriving Heisenberg Uncertainty principle, consider a function γ(t):
$γ(k,t)\equiv([t−(t)]−iκ[...
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Why cant we find exact position of an electron-Heisenberg Uncertainty principle?
I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION, page 88, and they say:
"We can conceivably measure the position of an electron by ...
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In the double slit experiment, when a particle is bombarded between two slits, why doesn't it "always" hit between the two slits and not pass at all? [duplicate]
The alignment is always towards the centre of the area between two slits.
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Explanation of spontaneous emission using uncertainity principle
How to understand spontaneous emission using Heisenberg's uncertainity principle? Why does it occur?
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Can the momentum operator have an imaginary expectation value?
I'm making examples of wave functions to incorporate in a QM exam.
I came up with the following wave function, which gives me some troubles:
$$\psi(x,0) = \begin{cases}
A(a-x), & -a \leq x \leq a,\...
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Relation between the lifetime of gain medium and laser frequency bandwidth in $\rm HeNe$ laser
When I am studying about Spiking phenomenon of lasers,
I found this
"spiking occurs for lasers where the upper-state lifetime is much larger than the cavity damping time. Gas lasers often ...
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Derive Heisenberg Uncertainty from General Uncertainty Principle
The General Uncertainty Principle of 2 Operators is given by
$$(\Delta X)^2\,(\Delta Y)^2 \geq\left(\dfrac{1}{2}\big\langle\{X,Y\}\big\rangle - \big\langle X\big\rangle \big\langle Y\big\rangle\right)^...
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Fourier Transform of a Wave Function relating to Position and Momentum
Why is it that, in quantum mechanics, the fourier transform of a wavefunction of the position of a particle is the wavefunction of it's momentum? I'm trying to learn about the uncertainty principle, ...
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Proving the uncertainty relation for the quantum covariance matrix
In quantum optics papers we often encounter this version of the Heisenberg uncertainly relation (for an $n$-mode quantum system):
$\sigma + \iota \Omega \ge 0$
Where $\sigma$ is the covariance matrix $...
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Wrong formulation of Heisenberg's uncertainty principle [closed]
My professor wrote this on the blackboard:
$$\Delta E\Delta t \leq \hbar$$
Isn't the $\leq$ sign wrong? Or is this "another" possible formulation of Heisenberg's uncertainty principle?
I am ...
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Heisenberg's Uncertainty principle: Position of momentum of Electron orbital
I need some clarification in my understanding of HUP with respect to electron in an atom. This is my current understanding,
Position of electron here means which orbit (Quatized orbits around nucleus)...
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Relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread
Consider a wave packet that satisfies the relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread appreciably in the time it ...
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Traversing between nodes (Zero Probability) in Quantum Mechanics
To elucidate the question I have in mind, let us consider a very simple QM system that has exact solution, say Particle in a 1D Infinite Well.
Since this is a well studied problem I will simply state ...
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Is there consensus among physicists that reality is fundamentally deterministic? [duplicate]
Does Heisenberg’s Uncertainty Principle mean that the universe cannot deterministically be predicted by observers, or does it mean that the universe is inherently indeterministic, meaning that the ...
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Correlation Amplitude in QM
The following is a section "Correlation Amplitude and the Energy-Time Uncertainty Relation" from Sakurai's Modern Quantum Mechanics book page 79:
Question:
Why does it state that the oscillations ...
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In quantum experiments are we measuring the quantum state of a system or are we measuring the effect of the measurement on the quantum state?
At the macro classical world, measurements in experiments when done correctly interfere very little with the state of the system under investigation.
As an example a digital ohmmeter with very high ...
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Deriving the equation for confinement kinetic energy
So confinement kinetic energy is given by $\frac{\hbar}{2m\triangle x^2}$. I'm a little confused with regards to how that it arrived at:
I started with the Uncertainty Principle : $\triangle p = \...
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Uncertainty principle when the expectation value of commutator is zero
I'm reading section 4.3 of Introduction to quantum mechanics written by David Griffits.
The book states that the product of the standard deviation of two components of angular momentum is greater than ...
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Conservation of momentum in single slit experiment
I am reading about the uncertainty principle and its stated that we can not simultaneously determine the position and momentum of a photon. But my question is, if you know the initial momentum of the ...
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Is this Fourier derivation of Heisenberg principle true?
I noticed that I can derive Heisenberg principle very easy.
$\begin{aligned}p=\dfrac{h}{\lambda }=\dfrac{h\nu }{\lambda \nu }=\dfrac{h\nu }{c}=h\nu \left( c=1\right) \\ Fourier\Delta v\cdot \Delta x &...
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Definition of a wave packet
In Shankar's QM book page 168, the author stated
a wave packet is any wave function with reasonably well-defined
position and momentum.
What does he mean by resonably well-defined position and ...
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Uncertainty of waves
Here in the pictures I have written about some question I have been thinking about a long time, what do you think?
Link to the chapter I am talking about:
http://www.its.caltech.edu/~matilde/...
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What is the maximum number of bounces a ball can be expected to make on another fixed ball of same radius on the ground?
In the book 'Quantum Mechanics' by Leonard I. Schiff, this question can be found at the end of chapter one. More specifically it asks:
A perfectly elastic ping pong ball is dropped in vacuum from a ...
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Since surface tension and area are conjugate variables, is there a uncertainty relation between them? $\Delta \gamma \Delta A \geq \text{constant}$
Since all conjugate variables have uncertainty relations like ;
$$ \Delta f \Delta t \geq \text{constant}$$
$$ \Delta \lambda \Delta x \geq \text{constant}$$
Etcetera, is there also a 'uncertainty ...
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The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?
I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
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Taking into account the Pauli Exclusion Principle, how many particles can you cram into a really small space?
I'm trying to understand the basic concept of the Pauli Exclusion Principle, but my former question here did not provide an answer. So let me rephrase it.
One way of describing the PEP is that you ...
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Why do we keep referring to the Heisenberg Uncertainty Principle in situations that we don't - and can't - know about? [closed]
In all of my reading in physics, I have been surprised by the number of times that I read "this can't exist" or "that can't exist" because of the Heisenberg Uncertainty Principle. ...
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Is there a minimum value different from zero for the uncertainty in momentum for a particle in a box?
Lately, I have been studying QM more deeply and I just discovered how many important subtleties the 'well-known' particle in an infinite potential well hides, which are precious for extending ...
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Heisenberg microscope for momentum
In the "Heisenberg microscope", the position of a particle is measured using a photon. The higher the photon energy, the better the precision in measuring the particle location is, but the ...
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Aharonov Bohm Effect Interaction Energy Interpretation: $\vec E_m = -∇Φ - D\vec A/Dt$?
The Wang paper "An experimental proposal to test the physical effect of the vector potential" proposes an experiment to decide between two interpretations of the Aharonov-Bohm effect:
“the ...
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Uncertainty principle manifesting in $j(j+1)$ vs $j^2$
To motivate my question, please consider a system with total angular momentum $j$. The fact that the largest eigenvalue of $J_z$ is $j$, while $J^2 = J_x^2 + J_y^2 + J_z^2$ has all eigenvalues equal ...
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How is the Heisenberg Uncertainty calculated value added to a measurement error bar?
It is not clear to me if the calculated HU for a specific experiment is added to the measured value Gaussian curve together with the statistical errors (i.e. added to the total error bar) of this ...
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Common eigenstate of incompatible observables
In many resources I have seen that incompatible observables cannot have a common eigenbasis set, but may share one or few eigen states. I followed the thread Can incompatible observables share an ...
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How is spooky action at a distance measured?
My recent background reading: https://www.science.org/content/article/more-evidence-support-quantum-theory-s-spooky-action-distance
I have been trying to understand how experiments actually measure ...
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What happens to the wavefunction of an electron trapped inside a nonreflective sensor-container? Does it prove HUP is only an epistemological limit? [closed]
Assume there is a spherical container of diameter of 1m, inside which at the center of which an electron is introduced at near zero velocity as limited by Heisenberg Uncertainty Principle(HUP) say at ...
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What is the value of Heisenberg Uncertainty in position $Δχ$ for a free electron at rest? [duplicate]
Any analytical calculation of this value included in a canonical answer would be nice!
We know according to HUP that:
$$
\Delta x \Delta p \geq \frac{h}{4 \pi}
$$
$\Delta x=$ uncertainty in position
$\...
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In uncertainty principle of waves
In uncertainty relations between freq. and time, if you had a part of a wave but not the entire cycle,(thus it is said that the frequency/wavelength is uncertain) couldn’t you based on the short curve ...
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In the case of a free wave function, does $|p| = E_k = 0 \mapsto |v|=0$?
This answer indicates that "it is not possible to talk about a particle 'stopping' or being 'stopped' in any meaningful or non-contrived sense" because of the Heisenberg indeterminacy ...
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Number-Phase uncertainty relation
I was trying to understand the Number-Phase uncertainty mainly following "A. Duncan, The Conceptual Framework of QFT", pages 223-233 and I got stuck into the definition of the operator
$$E = ...
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Can the Heisenberg Uncertainty Principle be explained intuitively?
I have heard several pseudoscientific explanations about the Heisenberg Uncertainty Principle and find them hard to believe.
As a mathematician mainly focusing on functional analysis, I have a ...
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How would you prove Heisenberg's Uncertainty Principle without making use of fancy language? [duplicate]
The title speaks for itself. What would be the down-to-earth meaning behind this principle beyond the incomprehensible mathematics and the abracadabrant lingo? (such as the wavefunction suddenly ...
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What is the relation between uncertainty and information obtained from a measurement?
For example, if a measurement gives a position with twice the uncertainty as another measurement, how much less information regarding position are you getting? In other words, if uncertainty doubles, ...
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Uncertainty principle in deformation quantization
Deformation quantization procedure is a well-known way to quantize a classical phase space (at least formally for Poisson manifolds which is known as formal deformation quantization). Although it is a ...
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Conceptually understanding an Ising-type transition
I am currently reading the following paper. The system consists of a chain of mesoscopic superconducting islands (aka a Josephson Junction array), but each island also contains a quantum wire that ...
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What is the theoretical limit on accuracy of an idealized photon detector?
I know that Heisenberg's Uncertainty Principle and the Observer Effect mean there is a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of particles (...
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Understanding the virtual states referenced in multiphoton absorption studies
The Heisenberg energy-time uncertainty tells us that we can have so-called virtual states between eigenstates as long as the lifetime of these states is at most:
$\tau = (\frac{h}{4 \pi E_v})$
Where $...
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