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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Why cant we find exact position of an electron-Heisenberg Uncertainty principle?

I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION, page 88, and they say: "We can conceivably measure the position of an electron by ...
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1answer
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Splitting the line and SNR of optical signal

In this lecture on optical resonance at around 5:28, the professor has drawn two plots, the top one is the time domain plot of pulse amplitude for a short duration of time while the bottom plot shows ...
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Is the Heisenberg uncertainty principle a consequence of the observer effect? [duplicate]

The question may seem stupid but I have heard from doubtful sources that the Heisenberg uncertainty principle results from the observer effect. I don't understand however how this works and i'm now ...
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Wave packet construction in Heisenberg's The Physical Principles of the Quantum Theory

I am trying to understand Heisenberg's development of a wave packet. This is the context: This is the statement confusing me (following eq #1): "Outside the boundary the component plane waves ...
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In the uncertainty principle, are $\Delta x$ and $\Delta p$ uncertainties? [duplicate]

I was thinking about a very old exam where the UP was expressed as $$\Delta x\Delta p\geq\frac{\hbar}{2}.$$ From what I understood in my measurement course, the uncertainty of a measurement model $Y$, ...
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When an electron hits a fluorescent screen mounted on a spring, why can't we get both position and momentum?

From the Heisenberg's Uncertainty Principle for position and momentum we know that, $x$ and $p$ of a particle cannot be measured simultaneously with arbitrary accuracy. $$\Delta x \Delta p \geq \hbar/...
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Is an infinite precise momentum measurement machine actually a teleporting device?

We know that, due to the uncertainty principle, the momentum and position of one object can be measured completely accurately at the same time. However, there is no theoretical limit if we only ...
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Any experiment preserving coherence up to the Heisenberg time?

The Heisenberg time is inversely proportional to the level spacing. In a many body system, it is huge. For a single- or few-body system, it might be not that large. So, so far, is there any experiment ...
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Are there simultaneous eigenstates of $L_x$ and $L_y$?

$L_x$ and $L_y$ don't commute since $[L_x,L_y] = i \hbar L_z$. From the uncertainty principle, we know that $\Delta L_x \cdot \Delta L_y \geq \frac{1}{2} \cdot |\langle i \hbar L_z \rangle|$. There ...
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Do the mean lifetimes of short-lived particles follow a Gaussian (or 'normal', or 'standard') distribution? When plotted?

For instance, the average 'mean' lifetime of a muon is just over 2 microseconds.... If I plotted many, many muon lifetimes after careful experimentation, would the chart show a Gaussian distribution? ...
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Most correct intuition for vacuum energies in interacting and non-interacting field theories

It seems like a lot of pop science gets thrown around when explaining vacuum energy. For instance, our QFT lecturer descried the non-interacting field theory vacuum energy as 'purely Heisenberg ...
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Strings and the Uncertainty Principle

I understand that the problem with fundamental particles is that they are $0$-dimensional and therefore infinitesimal in size. This seems unphysical and leads to infinities in calculations. The ...
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A problem with the uncertainty principle [closed]

It is postulated that the particle is described by a state vector $\Phi$, which is an element of Hilbert space. Let's suppose that there are two Hermitian operators $A$ and $B$, representing two ...
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Uncertainty principle and Fock states

While studying about single photon sources, I came across the following sentence on the related Wikipedia page The Heisenberg uncertainty principle dictates that a state with an exact number of ...
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Formulation of Heisenberg's uncertainty in terms of Shannon entropy

Heisenberg's uncertainty principle $$\Delta x \Delta p \geq h$$ asserts a fundamental limit to the accuracy versus uncertainty with which the values for the two canonically conjugate variables $\Delta ...
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Does this video from Veritasium imply that the uncertainty principle is false?

The video in reference : Is This What Quantum Mechanics Looks Like? At 4:47 to 5:10, he shows a situation meant to be an analogy to a quantum particle going through the double slit experiment and ...
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How to properly understand the commutator between angular momentum and angular coordinate? [duplicate]

When we study a single particle moving on a ring, we introduce the angular momentum $L$ and the angular coordinate $\phi$, which satisfy the following commutation relation $$ [L,\phi]=-i\hbar. $$ ...
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On the uncertainty principle [closed]

In the derivation of the Uncertainty principle, I am facing a problem in understanding how $\Delta E=\frac{2p\Delta p}{2m}$ is it $\Delta p^2 = p\Delta p + \Delta pp = 2p\Delta p$ or something else? ...
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Uncertainty Principle Violations?

I’m learning about Bells Inequality Experiment and have a question because the instructor in the video I am watching simply passed over something I found jarring. Ok, you have your entangled pairs of ...
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Phase space and uncertainty

In phase space every point represents both position and momentum. Isn't it against of Uncertainty principle?
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Explanation of momentum/energy arising due to uncertainty principle

While discussing the stability of hydrogen atom, specifically why the electron falling into the proton won't be the minimum energy state, the reason given is based on uncertainty principle. That the ...
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Can Heisenberg's uncertainty principle be used to prove the electron can't exist in the nucleus in this way?

This is the solution given in the textbook (my analysis below it): From my understanding, I believe this solution is wrong. My understanding is that the more accurately we know the position, the less ...
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Heisenberg’s Formulation of Quantum Mechanics and Particle Trajectories [duplicate]

In the article, under the history section, Heisenberg recounts a discussion with Einstein regarding Heisenberg’s matrix mechanics: “ He pointed out to me that in my mathematical description the notion ...
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The wave function collapse and uncertainty principle [duplicate]

If we measure the position of a quantum mechanical particle, then, according to the postulates, the particle's wave function collapses into a delta function and the measured result is one of the ...
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1answer
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Heisenberg Uncertainty Principle: How does this uncertainty compare to the energy of the transition?

An atom meets one of its electrons in an excited state. The average time that this remains in that state is $1 × 10^{−8}$ s to emit a photon of wavelength $620$ nm or $2$ eV energy. My questions are: ...
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The underlying cause of the heisenberg uncertainty theory [closed]

I don't fully understand the heisenberg uncertainty theory. Everything I don't know has transformed the theory into something i just don't understand one hundred percent. So my question is, Is there a ...
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Comparing 2 different uncertainty of KE of particle equations

I come across the uncertainty of KE of a particle in a box as: $$\Delta KE = \frac 12m[2v\Delta v\ +\ (\Delta v)^2]$$ I try to apply this equation by assuming an electron was placed in a 1-D box has a ...
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How to quantum tunnel a human? [duplicate]

I know this is purely theoretical, but I promise it is useful to me. Please reply even if you can answer only some of the points: Is the quantum tunneling probability connected to De Broglie ...
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1answer
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Question regarding the time (in)dependence of uncertainty/expectation values of position and location in Quantum Physics

I am trying to work out the time (in)dependence of uncertainty/expectation values of position and location in Quantum Mechanics. Let's take a simple example: a particle with mass m that moves one-...
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1answer
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Can a flux of electrons of speed below 10 m/sec pass an opening of 100 nm?

Suppose one has a flux of electrons with speed not exceeding 10 m/sec falling on a plate with an aperture of 100 nm. If the electrons can pass one would have a statistics of many electrons passed ...
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Electron separate from an atom -- still has same characteristics about location?

I have heard that a single electron has been trapped for a long time in I guess some kind of magnetic trap. I also understand that an electron in orbit around a proton in hydrogen atom is not really ...
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Understanding the math of Heisenberg's Uncertainty Principle

The Uncertainty principle is stated below: $$\Delta x.\Delta p\geq\frac{h}{4\pi}\tag{1}$$ Now, if we decrease the uncertainty in position $(\Delta x)$, the uncertainty in momentum has to increase to ...
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Confusion in uncertainty relation derivation

Nouredine Zettili derives the uncertainty relation in his book "Quantum Mechanics- Concepts and Application". While deriving, he reaches to an equation \begin{equation} |\langle\Delta A \...
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A question regarding commutators in quantum mechanics

I propose the following thought experiment: Suppose we have a beam of identically prepared electrons that is splits into two. The first goes through detector A that detects the $x+y$ where $x$ is the ...
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How to reconcile diffraction with the Heisenberg Uncertainty Principle?

When a particle of momentum $p$ (say $10^{-23}$ kg m/s e.g. an electron moving at 10 000 km/s) falls on a slit and passes through, what is its momentum after the slit? (One can also have a flux of ...
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Proof of Time-Energy-Uncertainty $\Delta H\frac{\Delta A}{|\frac{d}{dt}\langle A(t)\rangle|}\geq\frac{\hbar}{2}$

I am interested in mathematically proving the time-energy uncertainty relation by Mandelstamm-Tamm in a system seen in the Schrödinger-Picture (time-dependent states but time-independent operators). ...
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How much is the inherent quantum-mechanical uncertainty in the definition of the second?

Inspired by this other question. The second is defined such that the electromagnetic radiation whose energy equals the hyperfine splitting of the ground-state of the Cs-133 atom has a frequency of ...
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Can uncertainty of complementary variables be polarized?

The uncertainty principal is a bedrock of physics, and the oft-cited example of a pair of complementary variables is position and momentum. At least in the case, as with position and momentum, where ...
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1answer
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Deriving Uncertainty Relation for Canonical Commuting Observables from Schrödinger Uncertainty Relation

In case the names are not standard: \begin{equation} \sigma_{\hat{A}}^{2}\sigma_{\hat{B}}^{2} \geq \left\vert \frac{1}{2i} \left\langle \left[\hat{A},\hat{B}\right] \right\rangle \right\...
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Why don't wave packets disperse? [closed]

As the Uncertainty Principle suggests that $\Delta x\Delta p\geq h/4\pi$, a particle must have different velocities at any point in space within it's Gaussian distribution. Since wave functions ...
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How to calculate the accuracy limit for a particle in 1-dimensional closed box? Recursive systems. Heisenberg Uncertainity Principle

Assume a particle in a closed box. Both the particle and the box are confined to single direction/dimension. The cases are: The potential energy of the walls are infinite. The potential energy of the ...
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3answers
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Does an electron gain Energy passing through a small slit?

Suppose one has a flux of electrons with speed up to 10 m/sec (remark: the speed is not known exactly). The flux which can be modeled as a plane wave (or a semispherical) falls on a net of small ...
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Physical interpretation of Uncertainty

Uncertainty of an operator $\hat{A}$ when observing a state $|\psi\rangle$ is defined as \begin{equation} \Delta A_{\psi} = |(\hat{A} - \langle\hat{A}\rangle)\psi| \end{equation} Now assume that there ...
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1answer
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Where does an electron get energy from after passing a single slit?

An electron with a very low velocity $v_1$ after passing a narrow slit can get a very high velocity $v_2$ because of Heisenberg Uncertainty Principle. We place a passive detector to observe it, so the ...
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Does uncertainty principle apply to holes/gaps in matter?

Consider a hole in a semiconductor, or a missing atom in a crystal. Are their positions and momentum related by uncertainty principle? These factors would of course be determined by its surrounding ...
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Does a particle interact with walls of a slit?

It is kind of mystical that a particle goes through a slit and eventually changes its impulse due to Heisenberg uncertainty. Since the slit is an opening, it must not have interacted with it. Does it ...
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What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle

Assuming a laser beam going back and forth between two mirrors, what would happen if we keep bring the mirrors closer and closer to each other? Because after a certain width, we would be knowing both ...
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2answers
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What can be inferred about the mass of a particle from its decay width?

If we know the decay width of some particle, the mean life of the particle can be found via Heisenberg's uncertainty principle $$\Delta E\Delta t\sim\hbar$$ Is there a way to find the range of the ...
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Is this a valid way to derive the uncertainty principle?

In both Galilean and Special Relativity the laws of physics are the same in all reference frames, and similarly they are the same for all points in space. Not all objects have the same mass, so in ...
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Modern interpretation of "Heisenberg's microscope" heuristic [duplicate]

If I understand it correctly, the "Heisenberg's microscope" was a heuristic introduced by Heisenberg in order to explain the eponymous uncertainty principle. The idea would be that, when ...

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