The reason is that electrons (like all quantum mechanical objects) are wavelike. In an isolated hydrogen atom, the electron is in a spherically symmetric environment, so the solutions to the wave equation have to be spherical standing waves, which are the spherical harmonics. The wave frequencies have to be integer divisions of 2pi or else they would destructively interfere. (Technically each solution is a product of a spherical harmonic function and a radial function that describes how fast the electron wave decays vs distance from the nucleus)
What’s interesting is if the environment is not spherically symmetric (consider an electron in a molecule) the solutions to the wave equation (the electronic wave functions) are no longer spherical harmonics, even though we like to approximate them with combinations of spherical harmonic basis functions centered on each nucleus. It’s kind of like standing waves on a circular drum head (hydrogen atom) vs standing waves on an irregular shaped drum head
Of course the nucleus also has a wave nature and in reality this interacts with the electrons, but in chemistry and materials we mostly ignore this and approximate the nucleus like a static point charge from the elctrons perspective because the electrons are so much lighter and faster
Ah amazing - thank you for the response! I have a couple of related questions - is it that the non 2 pi frequencies exist, but they destructively interfere so we can't see them? My understanding is that the radial function for the electron is zero at the nucleus - there is no possibility of it being found there - but why is that the case?
While the treatment for methanol poisoning indeed includes ethanol, I don’t think your dosage suggestion is right. Your body would still have to process all the methanol, the job of the ethanol is just to slow down the reaction. If you suspect methanol poisoning you need the hospital, they will administer the ethanol intravenously and I think do dialysis to remove the methanol and the formic acid it metabolizes to (this is one of the toxins in ant venom)
There are groups that are actively working on automating conventional labs like this. Most of the efforts I know about use non-humanoid mobile robots or even just a six-axis arm on a rail and some lab space reconfiguration
This issue of accessibility is widely acknowledged in the academic literature, but it doesn’t mean that only large companies are doing good research.
Personally I think this resource mismatch can help drive creative choice of research problems that don’t require massive resources. To misquote Feynman, there’s plenty of room at the bottom
I like this analogy of always choosing “I’m feeling lucky” on Google, I feel like it clarifies a boundary between information retrieval and evaluation that gets blurred by language model summarizations. I’ve been frustrated with the LLM summary at the top of the Google search results for scientific topics because often the sources linked to don’t actually contain the information the summary is citing them for. Then I have a side quest of finding the right backing literature or deciding the summary was just wrong in the first place
There is https://orcid.org which is a persistent identifier for a researcher. It would be interesting if sending email to a researchers orcid handle resolved to their current institutional email address I guess?
My usual workflow is find the person on google scholar, find their uni/lab homepage, and hope they published their email there.
It’s all foreign guest researchers by the end of September, high risk countries by the end of March. Your first quote doesn’t imply the NIST sources for this article don’t have firsthand knowledge that this is coming, it’s just that it appears the lab management is avoiding putting things in writing
> Researchers from lower risk countries have been told they could lose access beginning in either September or December if at that point they have been at the lab more than 2 years or, under a waiver, 3 years.
The word "could" seems to conflict with "It's all foreign guest researchers by end of September."
If you think that's what he meant, then it's clear that Bob has made things incredibly ambiguous since we disagree. Do you think he might have written the article, and especially the headline, in such a way as to make it more clickable?
I don’t know why the author of the article wrote “could”, but I personally work closely with some non-high-risk-country NIST foreign guest researchers. It’s been filtered down verbally through the management chain that the end of this September is the re-review deadline, and it’s not been stated as a hypothetical.
Not a lot, but what is your point exactly? There are a lot of really Chinese scientists working in the US, and the ones who are postdocs and research scientists at NIST are apparently being pushed out at the end of this month. They’ve already been vetted for security concerns, so that justification is kind of thin.
How many Taiwanese, German, Indian, French, South Korean, etc scientists are working in the US? The ones working at NIST are facing being pushed out at the end of September.
This list of high risk countries is not new (with the exception of maybe Venezuela being recently added, I’m not sure). Researchers with these citizenships have faced extra security review before joining NIST for years, and last year the lab increased the level of security review for everyone (not just this list)
I can understand a clearly communicated need for additional security requirements. But NIST operates almost totally in open science mode, with the main exceptions of being industry cooperative agreements. I don’t think this move to shed international researchers by reneging on commitments from the lab has been at all justified from a security standpoint.
Your first reply was insightful, but this one is not a thoughtful take.
Power consumption and emissions are already increasing, and any regulatory changes in 2025 are not factored in to discussion of those numbers. It’s more interesting to discuss what these changes mean when they are a factor in 2026 and on.
What’s interesting is if the environment is not spherically symmetric (consider an electron in a molecule) the solutions to the wave equation (the electronic wave functions) are no longer spherical harmonics, even though we like to approximate them with combinations of spherical harmonic basis functions centered on each nucleus. It’s kind of like standing waves on a circular drum head (hydrogen atom) vs standing waves on an irregular shaped drum head
Of course the nucleus also has a wave nature and in reality this interacts with the electrons, but in chemistry and materials we mostly ignore this and approximate the nucleus like a static point charge from the elctrons perspective because the electrons are so much lighter and faster
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