Incoming links: Schrödinger equation
The idea the the wave function of a small observed system collapses "obviously" cannot be the full physical truth, only a very useful approximation of reality.
Because then are are hard pressed to determine the boundary between what collapses and what doesn't, and there isn't such a boundary, as everything is interacting, including the observer.
The many-worlds interpretation is an elegant explanation for this. Though it does feel a bit sad and superfluous.
Why are complex numbers used in the Schrodinger equation? Updated 2025-03-28 +Created 1970-01-01
Why is there a complex number in the equation? Intuitively and mathematically:
Necessity of complex numbers in the Schrödinger equation by Barton Zwiebach (2017)
Source. This useless video doesn't really explain anything, he just says "it's needed because the equation has an in it".
The real explanation is: they are not needed, they just allow us to write the equation in a shorter form, which is always a win: physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600
Why does 2s have less energy than 1s if they have the same principal quantum number? Updated 2025-03-28 +Created 1970-01-01
The principal quantum number thing fully determining energy is only true for the hydrogen emission spectrum for which we can solve the Schrödinger equation explicitly.
For other atoms with more than one electron, the orbital names are just a very good approximation/perturbation, as we don't have an explicit solution. And the internal electrons do change energy levels.
Note however that due to the more complex effect of the Lamb shift from QED, there is actually a very small 2p/2s shift even in hydrogen.
Split in the spectral line when a magnetic field is applied.
Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?
www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.
p splits into 3, d into 5, f into 7 and so on, i.e. one for each possible azimuthal quantum number.
It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.
Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".
Experimental physics - IV: 22 - Zeeman effect by Lehrportal Uni Gottingen (2020)
Source. This one is decent. Uses a cadmium lamp and an etalon on an optical table. They see a more or less clear 3-split in a circular interference pattern,
They filter out all but the transition of interest.
- youtu.be/ZmObNFAqkBE?t=165 passes the lines through a polarizer, which shows how orbital angular momentum is carried by photon polarization
- youtu.be/ZmObNFAqkBE?t=370 says they are looking at 1D2 to 1P1 changes.
Zeeman Effect - Control light with magnetic fields by Applied Science (2018)
Source. Does not appear to achieve a crystal clear split unfortunately.