# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...