This tag is for Heisenberg quantum mechanical uncertainty principle.

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Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
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Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq |\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\langle ...
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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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Are the authors saying that the observer effect plays no role in Bohr's thought experiment of the Heisenberg uncertainty principle?

Here is an excerpt from Eisberg & Resnick's Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Here is introducing Bohr's though experiment to establish a physical origin for the ...
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A few questions on wave packets and uncertainty relations

According to Cohen-Tannoudji the wave-function for a one-dimensional free particle can be written as $$ \psi (x,0)=\frac{1}{\sqrt{2 \pi}} \int g(k) e^{ikx} dk.$$ While $g(k)$ is not specified, there ...
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Why does temperature have no uncertainity?

Lets say I have an object A, with temperature $T$ and Hamiltonian $H_{A}$. Now take a thermometer B, with Hamiltonian $H_{B}$. Now when I put the thermometer in contact with A and do a measurement ...
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Does the electron confinement energy vary with temperature?

I was introduced the electron confinement energy. At room temperature thermal energy of a particle is about $k_B T$, where $T=298K$, giving about $25meV$. I was told that $E_\text{confinement}=50emV$, ...
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Luminal motion and the uncertainty principle

I had a thought the other day about a connection between special relativity and the uncertainty principle. According to special relativity, you need an infinite amount of energy to accelerate a ...
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54 views

Energy Conservation in Quantum System?

Let us assume, 2 same mass atoms are moving towards each other at equal velocity and they are in course to crash into each other - so what would happen when they do crash into each other? If we use ...
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Quantum properties of objects with zero velocity

Just curious: What would the Heisenberg Uncertainty Principle and De Broglie Wavelength be for a baseball that is not moving (i.e has zero velocity)? Also, since macroscopic objects like baseballs ...
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Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
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Heisenberg's uncertainty and $0 K$ temperature

when a body is subjected to $0 K$ temperature, it becomes rigid. hence if we see in terms of quantum the lattice vibration decreases, resulting in no change in the direction of the Random velocity, ...
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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 ...
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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 ...
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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 ...
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Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
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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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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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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 ...
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commutator to entropy in an uncertainty relationship?

Question: Does there exist a commutator to entropy in an uncertainty relationship? Similar Energy and time for instance.
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Quantum Gravity Singularity Question?

I am not a expert in QG (Quantum Gravity) or GR (General Relativity) for that matter so please forgive if I make any small mistakes, its just a curious question but I know that a singularity is a ...
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Minimum Uncertainty Wavepackets

I'm reading over some lecture notes on minimum uncertainty wavepackets in quantum mechanics, and I've come across a statement that I'm not entirely convinced by. My take on minimum uncertainty states ...
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Does Planck's constant imply limits to computing *results*

... I don't mean quantum effects limiting hardware fabrication sizing. Such small scales have for some time exhibited issues. Rather, along the lines of imagining the smallest possible divisions of ...
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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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commutators in an uncertainty relationship derived from a partition function?

The maximum information principle for the discrete case gives rise to a partition function (>>> see details here) $$Z(\lambda_1,\ldots, \lambda_m) = \sum_{i=1}^n \exp\left[\lambda_1 f_1(x_i) + \cdots ...
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Why position and momenta are fluctuating quantities?

In a coordinate basis we have $$\langle \Psi \mid \Psi \rangle = \int \prod_{i=1}^N d^3q_i |\Psi(\textbf{q}_1,\dots,\textbf{q}_N)|^2=1$$ This means that for any quantum state $\mid \Psi ...
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Are the particle-wave duality and the quantum uncertainty principle united?

In a recent paper by Patrick Coles, Jedrzej Kaniewski, and Stephanie Wehner at the Centre for Quantum Technologies at the National University of Singapore, they came to the conclusion that the ...
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Quantum relativistic effects

I was performing a thought experiment: let us assume an object is traveling so close to the speed of light that the length of the object is small enough for quantum effects to become noticeable to a ...
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Gedankenexperiment to derive the Robertson uncertainty relation without confusing it with the obersver effect

In the last years there seemed to be much activity on the meaning Heisenberg's uncertainty relation. The main point of the discussion was Heisenbergs noise-disturbance-relation (see: ...
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Uncertainty Principle - measuring momentum on one entangled particle, position on the other

If two entangled particles are sent far apart and then at exactly the same time the position of one, and the momentum of the other, is measured, won't this mean that, because the corresponding values ...
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Is there a Planck uncertainty?

There are theories which place lower limits on length, time and temperature. Is there a corresponding one for the lower limit for uncertainty? Is there a probability so small it cannot exist in this ...
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Huygens and philosophy of the slit

A single (narrow) slit diffraction pattern, can be explained/described classically with Huygens' principle (1678), and quantum mechanically with the Uncertainty principle. If the pattern on the screen ...
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Interesting (new to me) things in the exposition of Landau's book on QM

In section I.1 (The uncertainty principle), a principle I already know, the author suggests a "relaxing" picture (Unusual): "We have defined "apparatus" as a physical object which is governed, ...
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Question regarding waves squeezed

in one MOOC I am taking, the professor had a slide stating "when squeezed into a narrow space wave is amplified". I am not sure I understand what he meant by that, and I am trying to think into terms ...
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Naive Uncertainty principle for string theory

Is it possible, in some sense, that a naive uncertainly principle for string theory could be expressed as : $$ \Delta x_i \Delta p_j \Delta \sigma ~=~ \delta_{ij} \hbar \ell_s$$ where $\ell_s$ is ...
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Uncertainty Principle: Dropped dart

So when a dart of mass $m$ is dropped from a height $l$ the time to drop is $\sqrt{2l/g}$. With uncertainty the dart hits the ground at a distance $R$ where: $$R=\Delta x+\sqrt{2l/g}\space \Delta ...