Linked Questions

34
votes
4answers
9k views

Is there an infinite amount of wavelengths of light? Is the EM spectrum continuous?

The electromagnetic spectrum is a continuum of wavelengths of light, and we have labels for some ranges of these and numerical measurements for many. Question: Is the EM spectrum continuous such that ...
11
votes
2answers
2k views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
6
votes
2answers
2k views

Proving that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space

How can I prove that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space?
3
votes
4answers
7k views

Interesting relationship between diffraction and Heisenberg's Uncertainty Principle?

I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens' Construction but instead relies on Heisenberg's Uncertainty Principle: The ...
9
votes
6answers
534 views

Heisenberg uncertainty principle, what is it?

Heisenberg uncertainty principle (HUP), what is it? Before this gets marked as a duplicate, i've went through most of the posts here already, many of them multiple times. I've went through countless ...
2
votes
4answers
1k views

Why do radio waves spread out while higher frequency waves travel in beams?

Why is it that radio waves spread out in proportion to the square of the distance, while higher frequency electromagnetic waves, like microwaves, infrared waves, light, etc are able to propagate as ...
3
votes
2answers
662 views

What restrictions on time boundary conditions does it have to use Fourier transform to solve wave equation?

The wave equation can be solved using Fourier transform, by assuming a solution of the form of $$\mathbf{E}(x,y,z,t)~=~\mathbf{E}(x,y,z)e^{j\omega t}$$ and then reducing the equation to the Helmholtz ...
1
vote
1answer
915 views

relation between line width and life time

I don't see why the following relation should be correct. The scattering rate $R_s$ of atoms in a laser beam is $R_s=\frac{1}{T_s}$. $T_s$ is the time interval between the first and second ...
1
vote
2answers
238 views

Fourier transformation [closed]

I have recently studied Fourier and Laplace transformation in maths. I wanted to understand the utility in physics with some examples that requires this change in dimension and the reason why.
0
votes
1answer
135 views

Conditions for characterizing a wave as plane wave

Given a wave equation, say for example $\Psi(x,y,z,t) = a \cos\left(\omega t -\vec{k}\cdot \vec{r} \right)$, what conditions should be met for $\Psi$ to represent a plane wave?
1
vote
3answers
85 views

Uncertainty principle on optical fiber communication

While the calculations seem fine, I can't make sense of the solution to this problem. How can the uncertainty principle be used to tell us what the shortest pulse is? Wouldn't using it tell us the ...
1
vote
1answer
83 views

Errors and differentials

In the Heisenberg Uncertainty Principle $$ \Delta p \Delta x \geq \hbar/2$$ we write the inherent errors in measurement as $ \Delta p $ and $ \Delta x $ . Does these two errors behave the same as ...