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## New answers tagged uncertainty-principle

1

Heisenberg's uncertainty principle is $$\Delta x \Delta p \geq \hbar/2.$$ Since the well is of width $L$, you have a measure for the uncertainty on the position $\Delta x$. Then assume the lowest possible value for $\Delta p$, i.e. the one for which the above inequality becomes an equality. Lastly, use $E = \dfrac{p^2}{2m}$ to find an expression for $E$. ...

0

1) Uncertainty principle is momentum and position OR energy and lifetime, not energy and position. 2) If we confine the two particles in a infinite square well then they can only be in the well. Their wavefunctions go to zero at the boundaries. 3) True 4) False. Two particles can have the same energy. But thy have to be in two different states. For ...

1

Yes it fluctuates but it is a very small fluctuation. Note that unstable particles have a decay rate or width $\Gamma$ that is related to its lifetime $\tau$ by $$\Gamma=\frac{\hbar}{\tau}$$ when you measure the mass/energy of such particles in experiments you always get a Lorentzian or Breit-Wigner distribution like this from which you can measure the ...

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Take a simple quantum mechanical potential that describes an atom. The mass of the atom is fixed. Take hydrogen. The electron is in an orbital around the proton which is a probability distribution of its location in time and space: if you measure it, i.e. interact with it, where you may find it. Correspondingly there exists an energy width to the energy ...

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The Uncertainty Principle (UP) is not only a quantum mechanics property. There's a way to describe UP in an empirical approach (the famous Heisenberg microscope) but, from a mathematical (and historical) point of view, UP is intrinsically connected to Fourier transform (FT) properties. In fact if you assume that you have a gaussian wave packet in real space ...

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You may be confusing two things here. The uncertainty principle, which states that for any two observables $A$ and $B$ $$\sigma_{A}\sigma_{B} \geq \frac{1}{2}\left|\langle[\hat{A},\hat{B}]\rangle \right| \, ,$$ can be derived (see, for example, Proof of the Schrödinger uncertainty relation in Wikipedia). Canonical commutation relation $[x,p_x] = i ... 1 Although the Uncertainty Principle can be derived from other aspects of quantum mechanics, it is still regarded as a principle, rather than as a result or a relation, because it is an empirical principle of quantum mechanics. There is a complete discussion in the Stanford Encyclopedia of Philopsophy. 2 There are several mathematical proofs for the Uncertainty Principle, although it is also based out of intuition. A good, fundamental proof of the mathematical sort is found here: http://www.tjhsst.edu/~2011akessler/notes/hup.pdf. 7 This is an experimental physicist's answer: The linked article is careful to state: That means that conservation of energy can appear to be violated, but only for small values of t (time) Italics mine. Conservation of energy is an experimental fact that has been validated in innumerable experiments. This means, as far as the correspondence with ... 1 To summarize, assume hypothetically we managed to find a way in the future where we can have a look at an electron without disturbing it by measurement or causing its wave function to collapse, would the uncertainty principle still hold in such a case?? Why/Why not? To start with any measurement when looked at the quantum mechanical level involves ... 1 But in practice, is there any measurement that will NOT disturb the system at all? To prove that uncertainty is beyond measurement, we must design a measurement process that does not disturb the system. If such a process cannot be designed then the statement that "uncertainty is beyond measurement" cannot be experimentally tested. Isn't it? I don't know ... 1 It is not correct that the probability distribution of$x$and$p$are Gaussian in general. Take a simple system of a particle moving in some potential$V(x)$. The probability distribution of$x$is the square of the wave-function$\Psi(x)$of the particle, i.e. the probability of finding your particle in$[x,x+dx]$is$|\Psi(x)|^2dx\$. The probability ...

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I believe this can be attributed to the central limit theorem, which states that a large number of samples from a population with a well-defined variance will follow a gaussian distribution. The key idea is that because of quantum mechanics, we must treat both position and momentum as random variables; the uncertainty principle gives us a relation between ...

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