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.

Filter by
Sorted by
Tagged with
3 votes
1 answer
2k views

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. ...
2 votes
2 answers
938 views

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^...
3 votes
3 answers
113 views

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 ...
0 votes
0 answers
45 views

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 ...
0 votes
0 answers
89 views

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[...
0 votes
4 answers
171 views

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 ...
0 votes
0 answers
22 views

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.
0 votes
0 answers
20 views

Explanation of spontaneous emission using uncertainity principle

How to understand spontaneous emission using Heisenberg's uncertainity principle? Why does it occur?
21 votes
5 answers
10k views

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,\...
0 votes
0 answers
21 views

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 ...
0 votes
1 answer
54 views

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)^...
1 vote
1 answer
47 views

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, ...
3 votes
0 answers
28 views

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 $...
-1 votes
1 answer
318 views

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 ...
0 votes
1 answer
192 views

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)...
0 votes
0 answers
47 views

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 ...
2 votes
2 answers
152 views

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 ...
0 votes
5 answers
140 views

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 ...
0 votes
1 answer
553 views

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 ...
0 votes
1 answer
36 views

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 ...
1 vote
1 answer
186 views

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 = \...
0 votes
1 answer
27 views

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 ...
0 votes
1 answer
153 views

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 ...
0 votes
1 answer
44 views

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 &...
1 vote
1 answer
94 views

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 ...
0 votes
0 answers
19 views

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/...
4 votes
1 answer
293 views

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 ...
0 votes
0 answers
35 views

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 ...
0 votes
1 answer
52 views

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. ...
0 votes
2 answers
91 views

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 ...
-1 votes
2 answers
130 views

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. ...
3 votes
1 answer
62 views

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 ...
0 votes
1 answer
27 views

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 ...
5 votes
2 answers
346 views

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 ...
5 votes
1 answer
112 views

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 ...
0 votes
1 answer
48 views

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 ...
1 vote
1 answer
54 views

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 ...
4 votes
1 answer
525 views

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 ...
-6 votes
1 answer
91 views

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 ...
0 votes
0 answers
27 views

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 $\...
0 votes
1 answer
57 views

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 ...
0 votes
0 answers
13 views

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 ...
0 votes
0 answers
54 views

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 = ...
113 votes
18 answers
17k views

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 ...
-3 votes
1 answer
65 views

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 ...
1 vote
1 answer
323 views

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, ...
0 votes
1 answer
77 views

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 ...
0 votes
0 answers
33 views

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 ...
0 votes
0 answers
20 views

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 (...
10 votes
1 answer
2k views

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 $...

1
2 3 4 5
27