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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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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1answer
635 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi$. The probability density function describing how likely it is to find it in a given position is given by $f(x)=\left|\psi(x)\right|^2$. ...
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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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1answer
1k views

Zero-point energy amplitude calculation

On this page https://www.miniphysics.com/simple-harmonic-oscillator.html It is stated that for a linear restoring force of $F = -k \Delta x$, the total energy is $ E = K + U $ or rather $ \\ E = \...
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115 views

What is the maximum number of bounces a ball can be expected to make on another fixed ball of same radius on the ground?

In the book 'Quantum Mechanics' by Leonard I. Schiff, this question can be found at the end of chapter one. More specifically it asks: A perfectly elastic ping pong ball is dropped in vacuum from a ...
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101 views

Is there a Heisenberg Force?

If I read him correctly, in his book Quantum Theory, David Bohm argues that the reason an electron doesn't collapse into the nucleus is there is essentially a pressure due to the uncertainty principle ...
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126 views

Why does the uncertainty principle imply that empty space is filled with energy?

I read from this website that the uncertainty principle implies that seemingly empty space is filled with energy, called vacuum energy . The relevant equation I can think of is $$\Delta E\Delta t \geq ...
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200 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 ...
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608 views

The Heisenberg Uncertainty in Bose Einstein condensates

What happens to the Heisenberg uncertainty principle, when a system reaches the Bose-Einstein condensed state? In our statistical mechanics lecture, we derived the following formula for the fraction ...
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107 views

Underlying C*Algebra operators in standard quantum mechanics?

Linearity in standard quantum mechanics (QM) is the key to making the math possible in this field, but the presence of nonlinear operators in QM is what is more generally dealt with. Working with the ...
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Deriving a uncertainty inequality

Starting from $$(Δx) (Δp) \geq h/2$$ How does one derive $$a^2 (Δx)^2 + (Δp)^2 \geq a h~? $$
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62 views

Can current and voltage be linked by an uncertainty relation when electrons tunnel through a barrier?

Quantum tunneling has been shown to be linked to uncertainty relations for some observables involved in the system. For instance, if we consider electrons tunneling through a potential barrier it can ...
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43 views

What is the characteristic of a property?

Background: The following two observations are , in my understanding, pretty much accepted in quantum theory: Location is a property which is not preexisting but is established by measurement. It is ...
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50 views

Measuring the Momentum of a Quantum System using Position Measurements

A basic way to measure the momentum of a charged particle is to know that (classically) it follows a circular trajectory in a uniform magnetic field perpendicular to the plane of its trajectory, with ...
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54 views

How to get the Number Phase Uncertainty relation from the Energy time relation?

I can arrive at $\Delta H\Delta t \geq \frac{\hbar}{2}$, but how do I get from there to $\Delta N\Delta \phi \geq 1$ for the number states of light? I know we write $H = \hbar \omega (N + \frac{1}{2})...
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109 views

Are phase and particle (photon) number in QED conjugated variables?

I found in A. Zee's book "QFT in a nutshell" (1.edition) the interesting relation (8) respectively (9) in chapter III section 5 (p.173) which states that in a collective of non-relativistic bosons the ...
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58 views

Spread of the (smeared) field observable under time-evolution

Setup: Essentially, I'm interested in performing an analysis which is completely standard in QM, but I've never seen the analogue in QFT: Given I measure a system to have some value of its canonical ...
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87 views

In Cardy-Verlinde generalized uncertainty principle (GUP), how we know that the alpha is a constant of order one?

The GUP equation [1] is, $$\Delta x_i\geq\frac{\hbar}{\Delta p_i}+\alpha^2l_p^2\frac{\Delta p_i}{\hbar},$$ where $l_p$ is the Planck length. How do we know that $\alpha$ has a order of unity [1]? What'...
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137 views

Why is information conservation not restricted by the uncertainty principle?

The idea of information conservation seems to be: if all field equations/states of all particles/matter/waves at a certain time are known, all trajectories/waves can be backpropagated to retrieve all ...
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78 views

Connection Between Gaussian Fourier Transform and Minimal Uncertainty

The Fourier Transform of a Gaussian is a Gaussian. In QM, we get minimal uncertainty for a (normalized) Gaussian wave packet: $\Delta x\cdot \Delta p=\hbar /2$ Does the second fact has nothing to do ...
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115 views

QM result which implies equality in uncertainty relation

In Sakurai, there is a result in chapter 1 which states "the equality sign in the generalized uncertainty relation holds if the state in question satisfies $$\Delta A| \alpha \rangle = \lambda \...
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1answer
219 views

Uncertainty principle and digital camera

I recently got into a discussion in how far (miniaturized) digital cameras are affected by the uncertainty principle. Specifically the question was, whether the uncertainty principle is one of the ...
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354 views

Calculating Natural Broadening of Emission Lines

I'm trying to demonstrate the small effect of Natural Broadening as compared to other types of broadening (Doppler, Stark, van der Waals, etc.) and my calculations don't match the accepted values. My ...
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316 views

Simultaneous measurement of non-commuting observables without uncertainty

A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that $[\...
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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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221 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 ...
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317 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 p=\...
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720 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 ...
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110 views

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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Why cant we lower temperature to X where if an electron is observed it will be as if its an unobserved Temperate Y

Lets say the temperature is Y, and we want to observe an electron but if we do we will use a high energy light wave which will make it act more like a particle, so why dont we just lower the ...
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What is the relationship between the uncertainty principle and electron diffraction experiment?

I know that the uncertainty principle says that we can't measure the position and momentum at the same time but I still can't relate it to the electron diffraction experiment. Isn't that the electron ...
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2answers
30 views

Does Heisenberg uncertainty affect Snells law?

Assuming an ideal single frequency plane wave, we can determine the angle of retraction for the light beam. But the more I make my pulse shorter, the less certain I am in the frequency and thus the ...
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42 views

Quantum tunneling for bound states

In QM, take a particle in a bound state in $\mathbb{R}^n$ subject to a potential (need not be smooth and not necessarily bounded above, but is bounded from below, say, something that might roughly ...
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43 views

Average Energy in generic radial potential

Given a particle of mass $m$ moving in the radial potential $$ V(r)=-\frac{\lambda}{r^s} \quad, \ \lambda>0$$ I'm asked to compute the $L$-dependence (sign included) of the average kinetic, ...
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20 views

Is the time-energy uncertainty relation affected by the refractive index of materials?

For the time-energy uncertainty relation, is it or is it possible it could be affected by the refractive index of a material? In other words, if you have a material where the speed of light passing ...
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45 views

Uncertainty in wavelength of a photon emitted from atom

When an atom emits a photon, for some time the photon is close to its source, the atom, because it takes some time for the photon to move away from the atom. So during that time the uncertainty in the ...
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33 views

Generalized uncertainty principle and relevant energy scales

To include quantum gravity effects, some research works have suggested a deformation of the Heisenberg uncertainty principle. One particular model has, $$[\hat{x},\hat{p}]=i\hbar\left(1+\frac{\beta}{...
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1answer
79 views

Using the uncertainty principle to estimate energies in ground states

Suppose for example we want to find the minimum energy of a particle undergoing simple harmonic motion. In classical mechanics, the energy is: $$E = \frac{p^2_x}{2m} + \frac{1}{2} m \omega_0^2x^2$$ ...
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Is the cut-off energy in the calculation of the electron's self-energy associated with an electron size?

I have got two questions on the self energy/point particle concept of the electron: What do physicists exactly mean when they say the elementary particles (e.g. the electron) are point particles? ...
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1answer
71 views

According to quantum uncertainty, can an object transform into another object even with extremely low probability?

First of all I would like to point out that when it comes to quantum physics, I have very poor knowledge so please excuse me if I misuse some words to describe what I mean. My question is based on ...
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1answer
97 views

Where does $\pi$ come from in the Heisenberg equation?

In class today we were taught about Heisenberg’s equation, $$\Delta x\Delta p\ge\frac{h}{4\pi}. $$ Experience tells me that any time an equation involves pi, circles aren’t far behind. Obviously this ...
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Derivation of mass-lifetime relation in particle physics

How is the inverse relation between the lifetime and mass of a virtual particle derived? For example, it is said that the strong force is short range because its force carrier is massive, and hence ...
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23 views

Defining Angle between Observables consistently

Problem Setup: There is a nice proof of the heisenberg uncertianty principle using cauchy-schwarz given here Stated in variance form it is: $$ \sigma_x^2 \sigma_p^2 \ge \frac{\hbar^2}{4} $$ Now ...
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The validity of some “applications” of the uncertainty principle

Given a $L^2$ function $f$ with $\int_\mathbb{R}xf(x)dx=0$, define its variance to be $\sigma_f^2=\int_{\mathbb R}x^2f(x)dx$. The uncertainty principle states that $\sigma_f\sigma_\hat f\geq 1/4\pi$,...
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Derivation of Margolus-Levitin bound on the Quantum Speed Limit

In their derivation of the Margolus-Levitin bound on the "quantum speed limit" the authors make use of a trigonometric inequality $\cos x \ge 1-\frac{2}{\pi}(x+\sin x), \quad \forall x\ge0$ Is ...
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63 views

Hawking temperature, uncertainty principle and size of a black hole

I was playing with the Hawking temperature formula $$T_H = \frac{\hbar\ c^3}{8 \pi\ G\ M\ k_B}$$ and I thought it would be interesting to associate a velocity to this temperature: $$k_B\ T_H = \frac{1}...
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1answer
44 views

Heuristic for large $x$ behavior from small $q$ behavior of Fourier Transform

If I have a function $h(\mathbf x)$ which may be written $$h(\mathbf x)= \int \frac{\text{d}^d\mathbf q}{(2\pi)^d} \, h(\mathbf q) e^{-i \mathbf q \cdot \mathbf x}$$ and assume spherical symmetry, is ...
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64 views

Does uncertainty principle truly represent the “lower bound” of the information we can obtained from a pair of noncommunicable operator?

Background I: Suppose the commonly used non commuting operator $\hat p$ and $\hat x$. The uncertainty principle told us that $\sigma_p\sigma_x\geq \frac{\hbar}{2}$. In standard quantum mechanic ...
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1answer
20 views

Length and velocity of a pulse of particles

We are given a pulse of protons of duration $10^{-7}s$ and energy $2KeV$. I know I am supposed to use the uncertainty principle to solve this. I need to get the length and the indetermination of the ...
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39 views

Confused about using uncertainty principle to determining momentum

A question asks to estimate the energy of a neutron, if the neutron is composed of a proton and electron by using the uncertainty principle. The basic idea is to let x = 1 fm and calculate p using: $...