Tagged Questions
3
votes
1answer
33 views
Connection between a simple matter wave and Heisenberg's uncertainty relation
When looking at the wave function of a particle, I usually prefer to write
$$
\Psi(x,t) = A \exp(i(kx - \omega t))
$$
since it reminds me of classical waves for which I have an intuition ($k$ ...
0
votes
1answer
332 views
Gaussian wave packet
At our QM intro our professor said that we derive uncertainty principle using the integral of plane waves $\psi = \psi_0(k) e^{i(kx - \omega t)}$ over wave numbers $k$. We do it at $t=0$ hence $\psi = ...
7
votes
2answers
251 views
Was uncertainty principle inferred by Fourier analysis?
I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
1
vote
4answers
764 views
Reason for the Gaussian wave packet spreading
I have recently read how the Gaussian wave packet spreads while propagating.
see:
http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics
Though I understand the ...
5
votes
1answer
196 views
Relativistic contraction for a wave packet and uncertainty on momentum
Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
3
votes
1answer
261 views
wavefunction collapse and uncertainty principle
We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as ...
2
votes
1answer
133 views
How do you determine the degree of localization of a wavefunction?
Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
2
votes
2answers
177 views
Measurement and uncertainty principle in QM
The Wikipedia says on the page for the uncertainty principle:
Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two ...
1
vote
3answers
329 views
Why can't we know the speed, $\vec{v}(t)$, and position, $\vec{r}(t)$, of an electron (the two) at the same time $t$?
I've read something about this and I conclude that it happens because of the uncertainty principle. But I don't understand very well the meaning of that.
I mean, it's very abstract that the speed, ...
