Recent content by PeroK

As I said, my instinct is that the true area must lie within the given range. In this case, area could be 20.8, which is not ## 19\pm 1.5##. This is what happened with the blinds for my bedroom window. They were supposed to be whatever ##\pm 0.5## cm. But, they were +1cm more than I specified...

It's not a question of being precise. It's a question of the area definitely lying within the range given.

PS 20.5 is not an upper limit for the area. It would have to be ##19 \pm 2##, assuming the error must be symmetric.

My mathematical instinct is satisfied by ##19.4 \pm 1.5##. In this case, reducing the answer to ##19## plus or minus whatever doesn't make much sense. Say the problem involved buying stuff and you had to have enough. You'd definitely want 21 units and not 20 or 20.5. If 21 is not enough, then...

I'm not sure I know the expected answer, but I'd make the following observation. With that data, the area is between 17.92 and 20.88 units. That's definitely a range of nearly 3 units. It seems valid to say ##\pm 1.5##.

The expected value is the average. You always get an energy corresponding to the transition between two eigenstates. The measurement of the energy of these eigenstates is indirect. It's inferred from the spectrum. That's a common theme for many atomic phenomena. The theory is corroborated...

Only the ground state is stable. An atom in an excited state will emit one or more photons and reduce to the ground state. The same would be true of an superposition of excited states. The detection of a photon would be considered a measurement of the atom's energy and resolve the superposition...

She and her husband are not short of a bob or two!

The energy of a photon is inversely proportional to the wavelength. Hence $$\frac{E'-E}{E} = \frac{E'}{E}-1 = \frac{\lambda}{\lambda'} -1$$That is a much simpler calculation.

I get 17.8%. Note that energy is inversely proportional to wavelength.

It's better to use algebra and plug the numbers in at the end. You should be able to express the percentage energy loss as a function of ##\theta##.

PS it's actually a Spline function - continuous and piecewise polynomial in ##t##.

It's actually a continuous function.

Those two expressions are equal!

I was speaking to someone recently who is a professor in the social sciences. She has given up teaching and gone back to research only as she was fed up reading AI generated essays.