The owners of roads are incentivized to set reasonable rules so that people want to use their roads.

If you believe unverified information, you will lose money.

We have to distinguish between two types of creations. We'll discuss how the cost of coming up with both can be recouped without intellectual property and its awfulness.

Schrödinger equation for a one dimensional particle with $V=0$. The first step is to calculate the time-independent Schrödinger equation for a free one dimensional particle

Then, for each energy $E$, from the discussion at Section "Solving the Schrodinger equation with the time-independent Schrödinger equation", the solution is:Therefore, we see that the solution is made up of infinitely many plane wave functions.

Not the same as Hermite polynomials.

TODO. Can't find it easily. Anyone?

This is closely linked to the Pauli exclusion principle.

What does a particle even mean, right? Especially in quantum field theory, where two electrons are just vibrations of a single electron field.

Another issue is that if we consider magnetism, things only make sense if we add special relativity, since Maxwell's equations require special relativity, so a non approximate solution for this will necessarily require full quantum electrodynamics.

As mentioned at lecture 1 youtube.com/watch?video=H3AFzbrqH68&t=555, relativistic quantum mechanical theories like the Dirac equation and Klein-Gordon equation make no sense for a "single particle": they must imply that particles can pop in out of existence.

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This notation is so confusing! People often don't manage to explain the intuition behind it, why this is an useful notation. When you see Indian university entry exam level memorization classes about this, it makes you want to cry.

The key reason why term symbols matter are Hund's rules, which allow us to predict with some accuracy which electron configurations of those states has more energy than the other.

web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf puts it well: electron configuration notation is not specific enough, as each such notation e.g. 1s2 2s2 2p2 contains several options of spins and z angular momentum. And those affect energy.

This is why those symbols are often used when talking about energy differences: they specify more precisely which levels you are talking about.

Basically, each term symbol appears to represent a group of possible electron configurations with a given quantum angular momentum.

We first fix the energy level by saying at which orbital each electron can be (hyperfine structure is ignored). It doesn't even have to be the ground state: we can make some electrons excited at will.

The best thing to learn this is likely to draw out all the possible configurations explicitly, and then understand what is the term symbol for each possible configuration, see e.g. term symbols for carbon ground state.

It also confusing how uppercase letters S, P and D are used, when they do not refer to orbitals s, p and d, but rather to states which have the same angular momentum as individual electrons in those states.

It is also very confusing how extremelly close it looks to spectroscopic notation!

The form of the term symbol is:

The $2S+1$ can be understood directly as the degeneracy, how many configurations we have in that state.

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The libertarian opposition to government-funded welfare is based on of course, ideals of voluntaryism, but also on the efficiency of private entities. Simply giving the poor money is not the best way to end poverty. With private charities, the ones that can actually cause change in a neighbourhood will get donations, and inefficient ones won't. This will likely involve putting conditions on the money given, eg., that the able-bodied and able-minded must participate in education/employment. There's also the task of making such initiatives as efficient as possible.

If a pseudo-libertarian government were to forcibly collect money for welfare, it would be best to decouple the voting for the NAP-enforcing and welfare-providing branches, but there would still be a big problem.

If contributing to welfare was compulsory and the welfare provider was voted upon democratically, the votes of wealthy charity givers that want to see change would be drowned out by the votes of the poor that would prefer to receive money with no strings attached, and the votes of the upper and middle classes that want their contributions reduced. And if the voting isn't democratic, the system will be overthrown by the people. But reducing compulsary welfare via the votes of the upper and middle class is currently possible if all of them could be convinced that it is misplaced kindness.

The main concern people have regarding abolishing welfare is whether enough money will be donated to cover all poor people. The rich who can afford to donate large amounts already do, be it out of kindness or to acquire goodwill, and people would certainly donate a lot more if they didn't already have to pay half their money in income, property, value-added, excise, and numerous other taxes, for the "betterment of society". Libertarians believe that this, combined with the fact that the best performing charities will be the ones donated to, mean that poverty will be alleviated with less money needing to be spent.

We can't definitively prove this yet, so why not first test things out by slowly reducing the scope of government welfare? It must not all be cut suddenly, since time will be needed for the culture surrounding welfare to shift as people pay less in taxes, and for private charities to strengthen and become effective.

This example covered for example at Video 1. "Term Symbols Example 1 by TMP Chem (2015)".

Carbon has electronic structure 1s2 2s2 2p2.

For term symbols we only care about unfilled layers, because in every filled layer the total z angular momentum is 0, as one electron necessarily cancels out each other:

So in this case, we only care about the 2 electrons in 2p2. Let's list out all possible ways in which the 2p2 electrons can be.

There are 3 p orbitals, with three different magnetic quantum numbers, each representing a different possible z quantum angular momentum.

We are going to distribute 2 electrons with 2 different spins across them. All the possible distributions that don't violate the Pauli exclusion principle are:

m_l  +1  0 -1  m_L  m_S
     u_ u_ __    1    1
     u_ __ u_    0    1
     __ u_ u_   -1    1
     d_ d_ __    1   -1
     d_ __ d_    0   -1
     __ d_ d_   -1   -1
     u_ d_ __    1    0
     d_ u_ __    1    0
     u_ __ d_    0    0
     d_ __ u_    0    0
     __ u_ d_   -1    0
     __ d_ u_   -1    0
     ud __ __    2    0
     __ ud __    0    0
     __ __ ud   -2    0

where:

For example, on the first line:we have:and so the sum of them has angular momentum $0+1\hslash =1\hslash$. So the value of $m_L$ is 1, we just omit the $\hslash$.

TODO now I don't understand the logic behind the next steps... I understand how to mechanically do them, but what do they mean? Can you determine the term symbol for individual microstates at all? Or do you have to group them to get the answer? Since there are multiple choices in some steps, it appears that you can't assign a specific term symbol to an individual microstate. And it has something to do with the Slater determinant. The previous lecture mentions it: www.youtube.com/watch?v=7_8n1TS-8Y0 more precisely youtu.be/7_8n1TS-8Y0?t=2268 about carbon.

youtu.be/DAgEmLWpYjs?t=2675 mentions that ${}^{3}D$ is not allowed because it would imply $L=2,S=1$, which would be a state uu __ __ which violates the Pauli exclusion principle, and so was not listed on our list of 15 states.

He then goes for ${}^{1}D$ and mentions:and so that corresponds to states on our list:Note that for some we had a two choices, so we just pick any one of them and tick them off off from the table, which now looks like:

Then for ${}^{3}P$ the choices are:so we have 9 possibilities for both together. We again verify that 9 such states are left matching those criteria, and tick them off, and so on.

For the $m_S$, we have two electrons with spin up. The angular momentum of each electron is $1/2\hslash$, and so given that we have two, the total is $1\hslash$, so again we omit $\hslash$ and $m_S$ is 1.

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TODO definition. Appears to be isomers

Example: