Proof that the probability 1 is conserved by the time evolution:
It can be derived directly from the Schrödinger equation.
Bibliography:
Control theory Updated 2025-07-16
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
It's quite fun from a mathematics point of view!
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.
Data Updated 2025-07-16
These are obviously just a manipulative lie sales practice to make you want to buy at regular price.
Shame on you.
Similarly, recurrent Internet payments that give you one year's discount, and make you put up on your calendar to call them one year later threatening to give more discounts to be as cheap as competitors or I'm out.
DNA microarray Updated 2025-07-16
Can be seen as a cheap form of DNA sequencing that only test for a few hits. Some major applications:
DNA repair Updated 2025-07-16
Organelle Updated 2025-07-16
TODO clear attribution source:
Some people say, "Give the customers what they want." But that's not my approach. Our job is to figure out what they're going to want before they do. I think Henry Ford once said, "If I'd asked customers what they wanted, they would have told me, 'A faster horse!'" People don't know what they want until you show it to them. That's why I never rely on market research. Our task is to read things that are not yet on the page.
Stimulated emission Updated 2025-07-16
Photon hits excited electron, makes that electron go down, and generates a new identical photon in the process, with the exact same:This is the basis of lasers.
Charging for certification is fine. Creating exams and preventing cheating has a cost.
Another thing that is fine charging for is dedicated 1-to-1 tutor time. This is something Udacity is doing as of 2022.
www.investopedia.com/articles/investing/042815/how-coursera-works-makes-money.asp has a good mention:
MOOCs were first created by people with utopian visions for the internet. This means the idea for platforms like Coursera was likely conceived without a business plan in mind. Nonetheless, Coursera has managed to monetize its platform. It is worth noting, however, that monetization has lead to the effective elimination of the original MOOC idea, which is predicated on ideals like free and open access, as well as the building of online communities.
Coursera users must pay to engage with the material in a meaningful way and take courses for individualistic purposes. This has been a consistent trend among all major online education platforms.
and it links to: www.freecodecamp.org/news/massive-open-online-courses-started-out-completely-free-but-where-are-they-now-1dd1020f59/, very good article!
That is a fundamental guiding principle of OurBigBook.com. The educational content must be licensed CC BY-SA!
Perhaps the most reliable way of reaching this state is E-learning websites must allow students to create learning content.
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Engine Updated 2025-07-16

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