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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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1 answer
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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 \...
2 votes
1 answer
935 views

Uncertainty Principle and Bohmian mechanics

The Uncertainty Principle is a relationship between measurements of pairs of attributes, position and momentum, as well as energy and time. Perfect precision of one attribute's measurement leads to a ...
0 votes
3 answers
556 views

The definition of the complementarity principle

I am looking for a precise definition of the complementarity principle. It is rather briefly mentioned in my textbook, and I feel that authors have deliberately avoided defining it precisely. I'm a ...
0 votes
1 answer
295 views

Does increase in position uncertainty mean decrease in momentum uncertainty?

Suppose a Gaussian wavepacket describes a free particle. With increasing time, the uncertainty in position increases, and the particle moves in the $x$-direction. Does the increase in position ...
0 votes
1 answer
33 views

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 ...
0 votes
0 answers
64 views

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 ...
0 votes
4 answers
294 views

What happens to the uncertainty principle when I have a particle contained within an inelastic box?

Say I have a box made of inelastic material such that when a particle hits the box, energy is lost through heat. I then put a particle inside of this box and squeeze the box down. How does this not ...
2 votes
1 answer
54 views

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]\...
-2 votes
2 answers
100 views

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 ...
0 votes
3 answers
105 views

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 ...
1 vote
1 answer
215 views

How does the time-energy uncertainty principle give particles a non-well-defined mass?

It is example 3.7 from Griffith Quantum Mechanics 3ed: The $\Delta$ particle last about $10^{-23}\ \mathrm{s}$, before spontaneously disintegrating. If you make a histogram of all measurements of its ...
2 votes
1 answer
265 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 ...
1 vote
1 answer
290 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
716 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 ...
1 vote
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 ...
-1 votes
1 answer
43 views

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 ...
1 vote
1 answer
169 views

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 ...
-2 votes
1 answer
55 views

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 \...
0 votes
2 answers
79 views

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?
4 votes
3 answers
4k views

Heisenberg uncertainty principle and zero point energy

On my book is written: for a particle in an infinite square well (supposed 1D and large $a$) \begin{align} \Delta x\sim a \to& \text{Heisenberg uncertainty principle} \\ \to& \Delta p _\text{...
0 votes
0 answers
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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 ...
3 votes
5 answers
1k views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantum physics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
9 votes
1 answer
443 views

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 ...
1 vote
0 answers
28 views

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 ...
14 votes
4 answers
1k views

No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
1 vote
1 answer
62 views

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 ...
2 votes
1 answer
3k views

Prove: $(\Delta x)(\Delta \lambda) \geq \frac{\lambda^2}{4\pi}$

Currently I was going through the formula $$(\Delta x)(\Delta p)\geq\frac{h}{4\pi}$$ which is of course the enclosed form of Heisenberg’s Uncertainty Principle. But I also get this formula $$(\Delta x)...
-4 votes
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 ...
0 votes
1 answer
32 views

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 ...
1 vote
0 answers
47 views

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 ...
1 vote
2 answers
562 views

Aren't measurements in the Stern Gerlach experiment inherently intrusive to the states of particles?

The Stern Gerlach experiment that established the quantization of spin in a particular direction, according to my understanding, does so while inevitably affecting the particle. To conduct a ...
1 vote
1 answer
79 views

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 ...
-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 ...
0 votes
1 answer
535 views

Using Heisenberg's Uncertainty Principle to find the kinetic energy of an atomic particle

I'm working on a problem set for my modern physics course and a couple of the problems have asked me to use Heisenberg's uncertainty principle, given atomic nuclear radius (or uncertainty of an ...
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/...
1 vote
1 answer
52 views

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 ...
2 votes
4 answers
244 views

In quantum mechanics, is there an actual difference between 'observation' and interaction?

I apologize if this is just me misreading into things. So in some cases I've read that observation is simply interaction, only given a name that's somewhat misleading to the laymen. With the observer ...
3 votes
1 answer
278 views

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 ...
0 votes
1 answer
49 views

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 $h$/...
1 vote
1 answer
150 views

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, \...
0 votes
0 answers
76 views

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 &...
2 votes
2 answers
360 views

Electronic component of the Hamiltonian operator and uncertainty principle

This question has to do with the concept of uncertainty principle. The Hamiltonian operator has the electronic component that takes the inverse of the distance between any two electrons. My question ...
5 votes
1 answer
571 views

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 $$f=\left(\hat A-\langle A\rangle\right)|\Psi\rangle$$ $$...
2 votes
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 ...
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 ...
2 votes
1 answer
65 views

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. ...
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 $k$ ...
2 votes
1 answer
88 views

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 ...
0 votes
1 answer
205 views

What does it mean: $[\langle(\Delta x)^2\rangle\langle(\Delta p)^2\rangle](t)$?

I got following expression regarding linear harmonic oscillator in quantum mechanics, and I don't understand what it means. $[\langle(\Delta x)^2\rangle\langle(\Delta p)^2\rangle](t)$ $\Delta x$ ...
9 votes
6 answers
10k views

What is meant by "Nothing" in Physics/Quantum Physics?

I am not a phycisist, so please forgive my ignorance. This is related to my posts and this. I am trying to understand what is meant by the term "Nothing" in physics or Quantum Field Theory (QFT) since ...

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