12 questions linked to/from Heisenberg relation
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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.
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### 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?
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 ...