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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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Problem Deriving "The General Uncertainty Principle" in Section 5.7 of Susskind's "Quantum Mechanics"

I'm having a problem in section 5.7 of Susskind's "Quantum Mechanics, The Theoretical Minimum". Specifically, I'm trying to derive eq. 5.11, $$ 2\sqrt{ \langle \mathbf{A}^2 \rangle \langle \...
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Relative position when settings up a coordinate system, using the position of a quantum entity that is in a position superposition?

I am a bit confused about one aspect of quantum mechanics. I recognize that a particle does not necessarily (or ever) exist in one position eigenstate. Rather, it exists simultaneously in a linear ...
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Why can we use $|p| \approx\hbar /\langle x\rangle$ as an approximation?

In our lecture, the approximation for the zeeman energy shift is $$\frac{2e \vec{p} \vec{A}}{2m} \approx \frac{e \hbar B}{m}.$$ Here, symmetric gauge was used (therefore $A \approx r B$) and my ...
phein1's user avatar
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For any pure state, can I find a pair of non-commuting observables which saturate the uncertainty bound?

Given some pure state $|\psi\rangle$ we have the following bound on the uncertainty for two non-commuting operators $A$ and $B$ \begin{equation} \sigma_A\sigma_B\geq\left|\frac 1{2i}\langle[A,B]\...
Andrew Forbes's user avatar
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2 answers
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How does wave function collapse relate to uncertainty in position when measurement intervals approach zero? [closed]

In quantum mechanics, measuring the position of a particle causes the wave function to collapse, fixing the particle at a measured position. Given this collapse, how can it be claimed that as the ...
CuriousMind's user avatar
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3 answers
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Can the measurement problem be overcome? [closed]

I was listening to some physicists discuss the issues with measurement in quantum mechanics and some of the earlier philosophical repercussions. However in most cases where measurement affects a ...
hisairnessag3's user avatar
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2 answers
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Quantised optical cavities with non zero decay rate

The quantised electric field of an optical cavity can be described as a harmonic oscilator, $$\hat{H}_{\mathrm{c}}=\hbar\omega_{\mathrm{c}}\hat{a}^{\dagger}\hat{a}.$$ If the cavity mirrors are ...
Adrien Amour's user avatar
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Knowing all spin components at the same time [duplicate]

You can't know all spin components simultaneously due to the commutation relation (& Heisenberg's uncertainty principle): $[S_x, S_y] = i\hbar S_z$ But what if you know that $S_z=0$? Then that ...
Stallmp's user avatar
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Double-slit experiment with Buckyballs

Is it true that in the double-slit experiment with Buckyballs, performed in 1999 at the University of Vienna by Anton Zeilinger, a crystal (which scatters the launched molecules) was used instead of a ...
Pavel Borisov's user avatar
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Uncertainity in position in 1D potential box

In a question of a usual 1D box for a particle between $-L/2$ to $L/2$ i had to compute $\Delta x$ and $\Delta p$ for the particle. The solution used the formulas- $$\Delta x = \sqrt{\langle x^2 \...
SHINU_MADE's user avatar
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Why do heavier particles decay more faster or lives shorter? Is it due to the uncertainty principle?

If so, why does larger uncertainty in time imply longer lifetime? How does this link to the smaller uncertainty in energy of the massive particle?
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Derivation of Compton wavelength in Tong's QFT notes

On page 2 of David Tong's notes on QFT: http://www.damtp.cam.ac.uk/user/tong/qft.html, he makes use of Heisenberg's uncertainty principle to describe relativistic effects for a particle of mass $m$ in ...
ratchet411's user avatar
9 votes
1 answer
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Physical meaning of Zero-Point Energy

I know that a quantum system can never have 0 energy due the Uncertainty Principle, and its lowest energy is called the Zero point Energy. However, Energy is a relative quantity (atleast in classical ...
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Heisenberg uncertainty principle and QKD protocols

Some Quantum Key Distribution (QKD) protocols, like the well-known BB84, are said to be based on the uncertainty principle which I assume it to be the Heisenberg principle. This one states that two ...
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About uncertainty and the range of the nuclear interaction

When we calculate the mass of a pion, if let's say the range of nuclear interaction is 1 femtometer, we say $1\ \mathrm{fm}=c \Delta t$ First question is, why do we write here $\Delta t$, how is ...
Kutubkhan Bhatiya's user avatar
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3 answers
120 views

Is Heisenberg Uncertainty Principle (HUP) actually epistemic and not physical? [closed]

Is HUP just a way the physicists found to correct the unnatural concept and mathematical formalism of dimensionless-point elementary particles? Making these points more fuzzy and therefore giving ...
Markoul11's user avatar
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Interaction of light and charge leading to uncertainty in position?

To understand hysemberg uncertainty principle first I want to understand the uncertainty in position term . In hysemberg thought experiment he told that the uncertainty in position is due to the ...
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Photon and Observer effect

We cannot determine the position and momentum of a particle simultaneously with certainty . The product of uncertainty of them is greater than or equal to reduce planck's constant . The reason for ...
S K's user avatar
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1 answer
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Observation without interaction thought experiment [closed]

Here I am going to talk about a thought experiment that I have thought There is some isolated place in the universe where there is no EM field other than the field created by a moving point charge ...
Physics's user avatar
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1 answer
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Measuring Incompatible observables simultaneously of an entangled electron [duplicate]

Given that a pair of electrons are in the state $$\psi =\frac{ {|00}\rangle \pm {|11}\rangle }{\sqrt{2}}$$ (in the the spin-$x$ eigenbasis) . If we measure the spin along $x$ axis of one of the ...
veke's user avatar
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How does the Planck constant enter into the uncertainty principle?

In Stein & Shakarchi's Fourier Analysis, the Fourier transform of a Schwartz function $\psi$ is defined to be $$\hat{\psi}(\xi) = \int_{-\infty}^\infty \psi(x) e^{-2\pi i x \xi} dx$$ which gives ...
Drake's user avatar
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1 answer
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Derivation of Bremermann's Limit

The argument for Bremermann's limit, as I understand it, goes something like this: Begin with the time-energy uncertainty principle, as $\Delta E \Delta t \ge h$ (Other papers use other factors of $h$/...
Kaia's user avatar
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Density of states-phase uncertainty relation

I came across this uncertainty relation for Density of states $N$ and phase $\theta$ in "Introduction to Many-Body Physics" by P Coleman on Page 15, equation (2.20). $$\Delta N\Delta\theta &...
CuriousMind's user avatar
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1 answer
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Uncertainties $\Delta r$ and $\Delta p_r$ for the hydrogenoid stationary states

I'm interested in the general formulas that give the exact uncertainties $\Delta r$ and $\Delta p_r$ (the radial momentum) for all stationary states $|n,l, m \rangle$ (or $\psi_{nlm}(r, \theta, \...
Cham's user avatar
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5 votes
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Some questions about derivation of uncertainty principle

In Introduction to Quantum Mechanics by Griffiths and Schroeter, they derive the Uncertainty principle in the following way: First, they define $$f=\left(\hat A-\langle A\rangle\right)|\Psi\rangle$$ $$...
GedankenExperimentalist's user avatar
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0 answers
63 views

What does the Jacobi identity *mean* statistically?

Given that the commutator of a pair of operators shows up explicitly in the lower bound of the Robertson-Schrodinger inequality, I am wondering what, if any, statistical meaning/significance one can ...
hyportnex's user avatar
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3 votes
3 answers
318 views

Is measuring energy with arbitrary precision inherently impossible?

To see where this question comes from, consider a time independent Hamiltonian $H$ and an initial wave function $\psi(t=0,x)$. We can express time dependant wave function $\psi(t,x) = \sum_j e^{-iE_jt/...
Paradoxy's user avatar
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4 votes
0 answers
112 views

Uncertainty principle for incompatible observables whose probability distributions lack well-defined moments

The Heisenberg uncertainty principle states that the product of standard deviations (or variances) for incompatible observables has a non-zero lower bound (with a zero lower bound reserved for ...
Omid's user avatar
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If "borrowing energy for a short time" interpretation of HUP is wrong, then how are the ranges of fundamental forces explained?

I have heard many people mention that heisenberg uncertainity prinicple doesn't really allow 'violation of energy conservaiton for a short time'. i.e, virtual particles, are just a mathematical tool. ...
Luffy curious's user avatar
2 votes
0 answers
74 views

Connection between Quantum fluctuations and loops in the Feynman diagrams [closed]

I have a request. Please clarify these doubts for me: In the loops in quantum field theory there is a momentum $k$ which is integrated over. In a lecture, Professor Hong Liu says that this free $k$ ...
SX849's user avatar
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1 answer
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Why are the distances in real space and Fourier space inverses of each other?

I just came across a paragraph in a set of physics notes where they implicitly claim that imposing a cut-off $k<\Lambda$ to the modes in Fourier space is equivalent to smoothing the field in real ...
Wild Feather's user avatar
-1 votes
2 answers
111 views

Is there a physical cause of uncertainty? [closed]

The uncertainty principle is confusing me. Considering this image from the article: Is the particle believed to be physically moving with similar capriciousness in real space; and if so, what ...
jazamm's user avatar
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1 answer
113 views

The Heisenberg Uncertainty Principle (HUP) and "borrowing energy" [duplicate]

Often when physics students are introduced to the HUP for position and momentum, the interpretation is that you aren't able to measure position and momentum for a particle to arbitrary precision at ...
Depenau's user avatar
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0 answers
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Commutation of the operators used in definition of dispersion in Sakurai's proof of uncertainity [duplicate]

Given a Hermitian operator $A$, Sakurai (in his book "Modern Quantum Mechanics") defines $\Delta A$ as follows: $$\Delta A = A - \langle A\rangle$$ Where I believe $\langle A\rangle\vert\psi\...
SweepingBishops's user avatar
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1 answer
60 views

Particle physics question about uncertainty principle [duplicate]

I'm struggling with strong force interaction using particle-properties. In my book they give an example to explain this interaction using a Feynmandiagram of a proton and neutron and say that the ...
lynx_s's user avatar
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1 answer
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The more precisely we want to locate a particle in space, the more energy we will need to expend

The more precisely we want to locate a particle in space, the more energy we will need to expend. does this statement have a mathematical formulation? When studying quantum mechanics, I often found ...
potato's user avatar
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-3 votes
1 answer
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Doubts about Heisenberg principle

I am currently immersed in the study of quantum mechanics for an upcoming exam, specifically focusing on the demonstration of the Heisenberg Uncertainty Principle. While I believe I can successfully ...
user353399's user avatar
2 votes
0 answers
65 views

Can I use gravitational wave to break electron's double slit interference?

Electrons will perturb spacetime. So in principle in a double slit experiment, I can detect the gravitational wave emitted by the electron by a super-super capable detector at very far away, and ...
user74750's user avatar
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4 answers
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Is the statistical nature of quantum mechanics due to uncertainty principle?

Is the statistical nature of quantum mechanics due to position and momentum not defined for quantum particles? Update: I mean the uncertainty of any conjugate pairs.
iVenky's user avatar
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-3 votes
3 answers
129 views

Is matter-wave a consequence of the uncertainty principle? [closed]

The position and momentum of a particle are undefined because of the uncertainty principle. Does this result in matter-wave with wavelength given by the following equation? $ \lambda ={\frac {h}{mv}} $...
iVenky's user avatar
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-3 votes
1 answer
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Circumventing Heisenberg's Uncertainty Principle with Special Relativity...? [duplicate]

The Heisenberg Uncertainty Principle, formulated by Werner Heisenberg, states a fundamental limitation on the simultaneous precision with which certain pairs of complementary observables So what I ...
TanfeexUlhaqq's user avatar
3 votes
1 answer
170 views

Ground state of particle in a ring

In the ground state of a particle in a ring, the boundary conditions allow the particle to have energy equal to zero. This sounds that the momentum is completely defined and, according to the ...
Physical Chemist's user avatar
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0 answers
51 views

Entropy and uncertainty principle

I know that entropy depends on the total energy of a system. In the energy-time uncertainty, howeve, energy can be uncertain for an amount of time which is related to the uncertainty of energy by ...
Ahmed Samir's user avatar
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0 answers
53 views

Is the Uncertainty principle $ΔxΔp ≈ h$ an approximation? [duplicate]

The original paper by Heisenberg that discusses the Uncertainty principle has the following relation ΔxΔp ≈ h where x position, p momentum. Meaning, you can't do better than Planck's constant in the ...
iVenky's user avatar
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1 vote
1 answer
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Question regarding the uncertainty of momentum of particles [closed]

I have started learning QM and it says that we cannot deternine momentum and position or both of a particle acurately. There is an uncertainty in momentum ◇p and uncertainty in position ◇x . The ...
user avatar
1 vote
1 answer
56 views

How close to reality is my handwaving argument about Fabry Perot interferometers?

Under this answer to https://astronomy.stackexchange.com/q/55437/7982 I wrote a comment where propose the uncertainty inequality roughly written1 as $\Delta E \Delta t \ge h$ or for photons $\Delta \...
uhoh's user avatar
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1 vote
0 answers
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Is the space between plates, in Casimir effect, empty of momentum?

Please correct me if I am wrong. In Casimir effect, when two plates are brought very close to each other, there is a Force felt. This force is due to quantum fluctuations. The space between plates is ...
SacrificialEquation's user avatar
1 vote
0 answers
43 views

Find the uncertainty in the velocity of an electron and alpha particle respectively when they are located within 15×10^(-8) cm [closed]

recently I was solving questions on uncertainty principle but never came across questions involving system of particles like combination of electron and alpha particle. I wanted to understand how to ...
Lorenzo Torrent's user avatar
2 votes
2 answers
389 views

Uncertainty on the sum of two non-commuting operators

Suppose that I have an observable $$ \hat{E} = \sin(\alpha) \hat{Q} + \cos({\alpha}) \hat{P} $$ with $\hat{Q}, \hat{P}$ being non-commuting operators satisfying $$ [\hat{Q}, \hat{P}] = i \hbar $$ It ...
Nicolas Schmid's user avatar
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1 answer
58 views

The uncertainty principle and magnetic bar

As far as I know, the magnetic properties of a bar magnet is due to the alignment of electronic spins of all the atoms. According to the uncertainty principle the electronic spin is randomly up or ...
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