Experiments explained:
- via the Schrödinger equation solution for the hydrogen atom it predicts:
- spectral line basic lines, plus Zeeman effect
- Schrödinger equation solution for the helium atom: perturbative solutions give good approximations to the energy levels
- double-slit experiment: I think we have a closed solution for the max and min probabilities on the measurement wall, and they match experiments
Experiments not explained: those that the Dirac equation explains like:
The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.
Then, with that in mind, the general form of the Schrödinger equation is:where:
Equation 1.
Schrodinger equation
. - is the reduced Planck constant
- is the wave function
- is the time
- is a linear operator called the Hamiltonian. It takes as input a function , and returns another function. This plays a role analogous to the Hamiltonian in classical mechanics: determining it determines what the physical system looks like, and how the system evolves in time, because we can just plug it into the equation and solve it. It basically encodes the total energy and forces of the system.
The argument of could be anything, e.g.:Note however that there is always a single magical time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.
- we could have preferred polar coordinates instead of linear ones if the potential were symmetric around a point
- we could have more than one particle, e.g. solutions of the Schrodinger equation for two electrons, which would have e.g. and for different particles. No matter how many particles there are, we have just a single , we just add more arguments to it.
- we could have even more generalized coordinates. This is much in the spirit of Hamiltonian mechanics or generalized coordinates
The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.
Used to solve partial differential equation.
Some/all courses expire in 4 weeks: www.futurelearn.com/courses/intro-to-quantum-computing. Ludicrous.
Ciro thinks this is idiotic, and that Wizards should sell all cards individually with unlimited supply and all with the same prices, especially online where there are no printing costs. But because Wizards made the silly promise never to reprint certain cards with the reserved list in 1994, they can't even correct this mistake legally! (TODO maybe, see further discussion at: www.mtggoldfish.com/articles/contract-from-below-promissory-estoppel-and-the-reserved-list). There is however one simple solution: create and promote a new no reserve list format, and let reserve list formats rot away:One interesting outcome of this would be to have card cost limited formats. Penny Dreadful puts a super low limit, on individual cards, but it would be cool to have a max cost per deck version of it.
- www.youtube.com/watch?v=wIq0NWSLAJA Magic TV - A Look at Non Reserve List Legacy by ChannelFireball (2015). Notably, they suggest the workaround of printing very slightly differently functional reprints, e.g. "Snow covered duals". Genius.
- www.reddit.com/r/magicTCG/comments/8gtoj4/no_reserve_list_legacy/
A cool thing is when they printed Garth One-Eye, which allows you to make imaginary copies of some of those restricted list cards during play. This is the type of "flirting with the rules", that Ciro Santilli admires. The introduction of online-only cards such as XXX has pushed that even further as of 2021.
This was especially insane when Ciro was young and the Internet was not very widely available in Brazil yet, and Ciro did not know how to check the values of cards on online markets, and would trade cards with older much more knowledgable teenagers, based solely on his appraisal of a card's strength! Can you imagine how many young Timmys got ripped off in this manner, trading useless one million mana spells for ultra expensive black lotuses?
Another option we could pursue would be to make governments consider TCG pack opening a form of gambling, which it obviously is:
There is however one good solution to Magic's insane cost: watch people who have nothing better to do in their lives play on YouTube.
And as Internet formats dominate more and more, if they have any brains at will they will migrate to a subscription model where you pay to play for a given period of time, and have immediate access to all cards. It could even be a tiered access, with older formats being more expensive (more bugs to fix on different cards), but you must get access to all cards of a format at once.
The questions are: who is this Mark, and why does he have to go down?
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