2
votes
3answers
84 views

Measuring position and momentum at the same time?

In a non-relativistic quantum mechanical system in an infinite potential well. I try to measure the energy and the position of the system simultaneously. Since, the respective operators do commute ...
3
votes
2answers
67 views

What's the relationship between uncertainty principle and symplectic groups?

What's the relationship between uncertainty principle and symplectic groups? Does the symplectic groups mathematically capture anything fundamental about uncertainty principle?
5
votes
3answers
732 views

Didn't we mess up with the temperature?

The following passage has been extracted from the book "The Feynman Lectures on Physics-Vol l": The mean kinetic energy is a property only of the "temperature." Being a property of the ...
3
votes
0answers
57 views

Introductory derivations of Heisenberg uncertainty principle

I'm not an expert when it comes to quantum mechanics, so correct me wherever I'm wrong, but: I've always been a little bit bothered by introductory derivations of the Heisenberg uncertainty relations ...
0
votes
0answers
49 views

Uncertainty principle implies the non-deterministic universe? [duplicate]

Does the uncertainty principle imply the non-deterministic universe, or just the fact that our model of the universe, the one based on observation, can be at most non-deterministic, since we will not ...
0
votes
3answers
53 views

Do the same experiments yield different results due to the principle of uncertainty?

When thinking about small particles and their uncertainity, I've allways rather seen them being all over the place rather than randomly changing location. I would think that, in the same time, you'd ...
1
vote
1answer
56 views

Particle in a box: simultaneously bounded momentum and position

While writing an answer to this question, I started doubting about the interpretation of the uncertainty principle for the particle in a box. In the 1-dimensional particle in a box problem, explicit ...
14
votes
1answer
856 views

Is the Uncertainty Principle valid for information about the past?

My layman understanding of the Uncertainty Principle is that you can't determine the both the position and momentum of a particle at the same point in time, because measuring one variable changes the ...
1
vote
2answers
207 views

Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question. The ...
1
vote
2answers
146 views

Interesting relationship between diffraction and Heisenberg's Uncertainty Principle?

I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens' Construction but instead relies on Heisenberg's Uncertainty Principle: The ...
38
votes
9answers
2k views

Is the uncertainty principle a property of elementary particles or a result of our measurement tools?

In many physics divulgation books I've read, this seems to be a commonly accepted point of view (I'm making this quote up, as I don't remember the exact words, but this should give you an idea): ...
3
votes
1answer
57 views

Two explanations of non-zero atomic radius

I have came across two separate explanations for why atoms have a positive atomic radius (as opposed to electrons "collapsing" into the nucleus). The first is via Heisenberg Uncertainty Principle, ...
3
votes
2answers
469 views

Integral equations contradict The Uncertainty Principle?

I was reading about Integral equations, and I found this excerpt in Portuguese Wikipedia: "integral equations serve to determine the position in all instances of an object, if known, its ...
1
vote
2answers
239 views

What does this quantum experiment says about quantum world?

I am complete noob so please bear with me. I always read that in quantum world things exists as probability and only become one when they are observed...or wave collapses into particle. But there was ...
1
vote
2answers
108 views

Uncertainty principle

Think of a particle known to be trapped in a box of size $\Delta x$ and cooled down to near absolute zero. I know that attempting to measure the momentum of this particle repeatedly will give a random ...
1
vote
1answer
41 views

Atomic emissions and energy time uncertainty principle

Am I right, according the time-energy uncertainty principle, to say that an excited hydrogen atom in free space could emit photons with energies different from those possible by Bohr's calculations? ...
6
votes
3answers
165 views

Entropy and the uncertainty principle

According to the second law of thermodynamics, the total entropy of the Universe must always increase after any interaction (as I understand). So in the hydrogen atom, the electron has a high ...
11
votes
2answers
435 views

Why uncertainty principle is not like this?

In Griffiths' QM, he uses two inequalities (here numbered as $(1)$ and $(2)$) to prove the following general uncertainty principle: $$\sigma_A^2 \sigma_B^2\geq\left(\frac{1}{2i}\langle [\hat A ,\hat ...
1
vote
0answers
66 views

Heisenberg Uncertainity Principle

If any senior member of the group has access to the book, The Physical Principles of Quantum Theory by W. Heisenberg, then please help me in understanding the first section of chapter 2 where he gives ...
3
votes
0answers
162 views

“Derivation” of the Heisenberg Uncertainty Principle

Ok, so I posted this in the mathematics StackExchange, but got no response. The question I outline below is my textbook's "derivation" of the Heisenberg Uncertainty Principle. The "derivation" my ...
1
vote
1answer
61 views

Does the energy-time uncertainty principle require energy levels to have finite width?

The uncertainty principle also has the form: $\Delta$$E$$\Delta$$t>h/2\pi$ Now this should mean that the thickness of the lines we draw in the energy level diagrams to show energy change undergone ...
1
vote
2answers
150 views

Can we describe mathematics using filters and matrices? [closed]

Can mathematical filters or ultrafilters be used to predict quantum physics 'events' as accurately as using matrices like Schrodinger did? Is there a way to explain some of the predictive power of ...
4
votes
1answer
136 views

Time-Energy Uncertainty Principle and Operators

In most of examples, I notice that uncertainty principle for time & energy is given between mass & lifetime. The UP for time and energy is $$ \Delta t\,\Delta E\geq\frac h{4π} $$ where $$Δt ...
1
vote
1answer
50 views

Position and potential Energy

Why are the position and potential energy of a particle able to be measured precisely in Quantum Mechanics? I mean why do they commute with each other?
0
votes
1answer
47 views

Uncertainty Principle Upper-bound?

In quantum mechanics, is there an upper bound for the uncertainty principle? I know that quantum harmonic oscillator (QHO) has the uncertainty relation $\sigma_x\sigma_p = \hbar(n+1/2)$, but I think ...
8
votes
1answer
169 views

Question on Uncertainty Principle

I have read about the uncertainty principle. And it applies to electrons. Then how is it that we can get exact tracks of electrons in cloud chambers?? That is to say that how is it that the position ...
0
votes
1answer
109 views

Question on Quantum Harmonic Oscillator

My textbook claims that the uncertainty in position of the particle in a quantum harmonic oscillator is $\frac{A}{\sqrt{2}}$ and the uncertainty in the particle momentum is $\frac{p}{\sqrt{2}}$ ...
10
votes
6answers
2k views

If I drop a leaf twice from the height of a tree in a completely controlled environment, will the trajectory in each case be the same?

Putting my question in other words, can earth form again if a similar initial universe condition is given? The uncertainty principle says that we cannot tell with certainty the position of a particle ...
1
vote
2answers
77 views

Uncertainty principle in Quantum mechanics

The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously. Is this because the uncertainty is the natural characteristic or it is ...
2
votes
0answers
29 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
2
votes
0answers
111 views

The Uncertainty Principle and Energy Nonconservation

The uncertainty principle is listed in most textbooks and articles as $$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$ This can be derived in many ways in many different settings, most of them involving ...
0
votes
0answers
50 views

Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
0
votes
1answer
357 views

Energy conservation limited by uncertainty principle

The way I learned it from practicing Fourier analysis and signal processing besides quantum mechanics, is that Energy conservation cannot be achieved in short time scales, and that limits energy ...
0
votes
2answers
145 views

What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's ...
1
vote
1answer
125 views

Heisenberg's uncertainty principle - Planck's (reduced) constant divided by two or not? [duplicate]

The most common form of Heisenberg's uncertainty principle I've seen online is $$ \Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$ However, I also regularly see $$\Delta x \Delta p ~\geq~ \hbar. $$ ...
1
vote
1answer
165 views

Relating Schrödinger's Wave Equation and Heisenberg Uncertainty Principle

A homework question that I don't conceptually understand: A quantum particle of mass M is trapped inside an infinite, one-dimensional square well of width $L$. If we were to solve Schrodinger's wave ...
0
votes
1answer
56 views

Doesn't the uncertainty principle mean all particles with identical energy are indistinguishable and hence have an amplitude for exchange?

I wonder if someone could tell me where my logic is going wrong here? If two particles both have definite energy, then they have indefinite position. As their positions could literally be anywhere ...
1
vote
3answers
107 views

Quantum entanglement and uncertainty

I have a question about measuring entangled particles and the uncertainty principle. I know that this has been asked before, but I am still not clear on the explanations, so I will try to explain why ...
8
votes
4answers
742 views

Is the uncertainty principle axiomatic or derived?

To take an example, Feynman Lectures Vol 3 13-1 Let's think of an electron which ban be in either one of two positions [...] There are two possible states of definite energy for the electron. ...
5
votes
1answer
609 views

Does the uncertainity principle violate the law of conservation of energy?

What is the scientific view of the beginning of universe? Quantum fluctuation seems to contradict with the law of conservation of energy. Uncertainity Principle does seem to violate the Law of ...
0
votes
0answers
75 views

Uncertainty principle and commutation relations [duplicate]

What connection exists between the uncertainty principle and commutation relations amongst the operators representing observables in Quantum Mechanics?
2
votes
0answers
84 views

Momentum representation of a state

I am trying to figure out the momentum representation of the state which has the properties $$\langle \psi |\hat q |\psi \rangle=-q_0,$$ $$\langle\psi|\hat p|\psi \rangle=p_0, $$$$\Delta q\Delta ...
1
vote
2answers
183 views

Gaussian Probability Distribution?

The uncertainty principle states that, $$\sigma _{{x}}\sigma _{{p}}\geq {\frac {\hbar }{2}}.$$ It is mentioned from many sources that the probability distribution of the particle position and ...
2
votes
2answers
292 views

Is it only the ground state of the quantum harmonic oscillator that has the minimum uncertainty product?

We know that the uncertainty product of general states is bounded by the inequality described by Heisenberg's uncertainty relation. And the ground state of the quantum harmonic oscillator falls under ...
2
votes
1answer
69 views

Theoretical Upper Bound on Processor Speed?

Barring aside considerations such as heat dissipation, capacitance, etc... (aka any sort of technological issue) what is the fastest speed of a processor? I am told that at distances of 1 planck ...
0
votes
0answers
87 views

Intuitive explanation for angular momentum uncertainty?

The basic commutator relation $$[J_1,J_2]=i \hbar J_3$$ of quantum mechanics yields the uncertainty relation $$\Delta(J_1)\Delta(J_2)\ge \frac{\hbar}{2}|\langle J_3\rangle|.$$ However, unlike the ...
0
votes
1answer
234 views

Can Zeno's Dichotomy Paradox be Resolved with Quantum Mechanics?

I would like to start off by saying this is not a philosophical question. I have a specific question pertaining to physics after the following explanation and background information, which I felt was ...
0
votes
1answer
101 views

Finding $\Delta p$ for discontinuous wave function

So I have a triangle Wavefunction defined as: $$\psi(x)=\begin{cases}x &0<x<\frac{L}{2} \\ L-x &\frac{L}{2}<x<L\end{cases}$$ When I try to find the uncertainty in momentum, I ...
0
votes
0answers
39 views

Quantum Mechanics and General Relativity in Macroscopic Level [duplicate]

Hi I read a book yesterday.The book was Brian Greene's The Elegant Universe. I learned that uncertainty principle affects space-time very microscopic levels and this affection makes conflict in ...
0
votes
1answer
100 views

Quantum state with zero standard deviation of position operator

Is any quantum state $|\psi\rangle$ possible such that the standard deviation $\sqrt{\langle\psi|(\Delta\hat{x})^2|\psi\rangle}$ of the position operator $\hat{x}$ is zero? If not, why?