Schrodinger

[Alison Le 2E]

Hi! Can someone please summarize the relationship between Schrodinger's equation, wave functions, and orbitals? Thank you!

[Vivek Chotai 2C]

So let's say there's this dude named schrodinger who made a magic equation. His equation takes in the quantum numbers of an electron as inputs and spits out their wave functions as an output. Now these wave functions of the electrons are called the orbitals (I think because they are thought to orbit the nucleus, but kinda do so in a wave trajectory).

With these orbitals, which remember are still functions, we square and then graph to find the the electron density at a specific point. By specific point, I mean in the x y z plane, because those were the inputs to the schrodinger dude's equation. So squaring his magic equation will tell me what the chance is that the electron is at that specific point that I chose, based on the quantum numbers. And since we squared his magic equation, we won't get any negative outputs (which is good because then we don't have negative probability).

Going back to the magic equation, turns out if we take its double derivative, we can figure out the energy of the electron. And if we know the energy of the electron at a specific level, then you can calculate the difference in energy levels of a certain atom. And then maybe you can even say that based on the energy difference, you know what specific atom the electron is a part of!