This tag is for Heisenberg quantum mechanical uncertainty principle.

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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 ...
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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 ...
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“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 ...
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1answer
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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 ...
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1answer
100 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 ...
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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 ...
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1answer
43 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?
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1answer
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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 ...
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4answers
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Why is the Heisenberg uncertainty principle stated the way it is?

I spent a long time being confused by the Heisenberg uncertainty principle in my quantum chemistry class. It is frequently stated that the "position and momentum of a particle cannot be ...
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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 ...
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1answer
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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 ...
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1answer
80 views

The Physical Meaning behind a Commutator [duplicate]

I've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of ...
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1answer
66 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 $\frac{p}{\sqrt{2}}$ ...
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6answers
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Why can't we use entanglement to defy Heisenberg's Uncertainty Principle?

In principle, it is possible to entangle any property of two particles, including speed and momentum. Surely then, this could be used to defy the Uncertainty Principle, which states that the momentum ...
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2answers
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How can a clock work if the uncertainty principle is true?

If the uncertainty principle and Copenhagen Interpretation are true, then how can a clock tick? Supposedly particles can do all sorts of things when not measured, then how can they be formed into ...
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2answers
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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 ...
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1answer
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How do you measure a particle's postion or momentum?

This question is about the Uncertainty Principle $$\sigma_x \sigma_p ~\ge ~\frac{\hbar}{2}.$$ Looking at the maths, I understant why the uncertainty in the poistion increases as the uncertainty in ...
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0answers
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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 ...
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0answers
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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 ...
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2answers
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Does measuring the exact position of a ball destroy the ball

If you have a macroscopic ball (say, a tennis ball) and you (hypothetically) try to measure the exact position of the center of that ball by measuring the exact positions of the atoms making up the ...
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4answers
369 views

Why complex functions for explaining wave particle duality?

I have this very bad habit of going to the scratch, discarding all the developments of a theory and worldly knowledge, and ask some fundamental (mostly stupid and naive, as some may say) questions as ...
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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 ...
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1answer
128 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 ...
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2answers
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Heisenberg Uncertainty Principle: Which formula is correct?

Some websites and textbooks refer to $\Delta x \Delta p \geq \frac{\hbar}{2}$ as the correct formula for the uncertainty principle whereas other sources use the formula $\Delta x \Delta p \geq \hbar$ ...
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1answer
79 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 $$\Delta x \Delta p ~\geq~ \hbar. $$ ...
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2answers
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Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes ...
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1answer
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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 ...
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1answer
263 views

Change In Momentum In Uncertainty Principle

The most basic explanation for the Heisenberg Uncertainty Principle is that the momentum and position of a quantum particle is not very distinct when an attempt is made to measure them together. But ...
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45 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 ...
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1answer
40 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 ...
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2answers
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Energy of quarks and the mass of the proton

We know that energy of quarks inside the proton can not be exactly fixed because if it,the 'proton decay' must not be exist. My question is if the energy of quarks inside the proton is not exactly ...
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4answers
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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. ...
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1answer
365 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 ...
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Uncertainty principle and commutation relations [duplicate]

What connection exists between the uncertainty principle and commutation relations amongst the operators representing observables in Quantum Mechanics?
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72 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 ...
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4answers
278 views

Is uncertainty principle a technical difficulty in measurement?

I have searched for an answer to this question on physics SE but I have not seen a question in which it is addressed properly. Please let me know if there is an answer already. My question briefly ...
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2answers
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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 ...
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2answers
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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 ...
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1answer
55 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 ...
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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 ...
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1answer
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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 ...
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Could the Heisenberg Uncertainty Principle turn out to be false?

While investigating the EPR Paradox, it seems like only two options are given, when there could be a third that is not mentioned - Heisenberg's Uncertainty Principle being given up. The setup is this ...
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1answer
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Why $\Delta x \Delta p_x$ for stationary states increase linearly with n?

Harmonic Oscillator $\displaystyle \Delta x\Delta p_x = \hbar (n+\frac{1}{2})$ Particle in a box $\displaystyle \Delta x\Delta p_x = \frac{\hbar}{2} \sqrt{(\frac{n^2\pi^2}{3}-2)}$ We notice ...
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2answers
109 views

Physical meaning of uncertainty principle + question on symmetry

A question on the Uncertainty principle. So we know that it says (for position and momentum) that: $$ \Delta x \Delta p \ge \hbar/2 $$. Where $\Delta p = \sqrt {<p^2> - <p>^2 }$ and ...
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1answer
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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 ...
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0answers
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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 ...
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1answer
84 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?
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1answer
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Uncertainty on a single observable measurement

Heisenberg Uncertainty Principle states (in the form of the Robertson-Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement ...
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1answer
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Heisenberg uncertainty principle and minimum energy

In an exercise, given the average lifetime $\tau$ of a particle, the author estimates the minimum energy using the uncertainty principle formula : $\Delta E \Delta t \geq \hbar/2$, assuming $\Delta t ...
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On an Uncertainty Relation for Angular Variables

I'm looking for a proof of the Angular Momentum - Angle uncertainty relation $$\frac{\Delta L \Delta \theta}{1-(3/\pi^2)\Delta \theta^2} \geq \frac{\hbar}{2}$$ which does not involve solving the ...