Incoming links: ViaScience
Besides the angular momentum in each direction, we also have the total angular momentum:
Then you have to understand what each one of those does to the each atomic orbital:
- total angular momentum: determined by the azimuthal quantum number
- angular momentum in one direction ( by convention): determined by the magnetic quantum number
There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 1. "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.
TODO experiment. Likely Zeeman effect.
Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)
Source. Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!
Experiments explained:
- spontaneous emission coefficients.
- fine structure, notably for example Dirac equation solution for the hydrogen atom
- antimatter
- particle creation and annihilation
Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.
- Lamb shift
- TODO: quantization of the electromagnetic field as photons?
The Dirac equation is a set of 4 partial differential equations on 4 complex valued wave functions. The full explicit form in Planck units is shown e.g. in Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=1010:Then as done at physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600 from why are complex numbers used in the Schrodinger equation?, we could further split those equations up into a system of 8 equations on 8 real-valued functions.
Equation 1.
Expanded Dirac equation in Planck units
. Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)
Source. PHYS 485 Lecture 14: The Dirac Equation by Roger Moore (2016)
Source. Clear experiment diagram which explains that the droplet mass determined with Stoke's law:Video 1.
Quantum Mechanics 4a - Atoms I by ViaScience (2013)
Source. American Scientific, LLC sells a ready made educational kit for this: www.youtube.com/watch?v=EV3BtoMGA9c
Here's some actual footage of a droplet on a well described more one-off setup:
This American video likely from the 60's shows it with amazing contrast: www.youtube.com/watch?v=_UDT2FcyeA4
Used to explain the black-body radiation experiment.
Published as: On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.
Quantum Mechanics 2 - Photons by ViaScience (2012)
Source. Contains a good explanation of how discretization + energy increases with frequency explains the black-body radiation experiment curve: you need more and more energy for small wavelengths, each time higher above the average energy available.Quantum entanglement is often called spooky/surprising/unintuitive, but they key question is to understand why.
To understand that, you have to understand why it is fundamentally impossible for the entangled particle pair be in a predefined state according to experiments done e.g. where one is deterministically yes and the other deterministically down.
In other words, why local hidden-variable theory is not valid.
How to generate entangled particles:
- particle decay, notably pair production
- for photons, notably: spontaneous parametric down-conversion, e.g.: www.youtube.com/watch?v=tn1sEaw1K2k "Shanni Prutchi Construction of an Entangled Photon Source" by HACKADAY (2015). Estimatd price: 5000 USD.
Bell's Theorem: The Quantum Venn Diagram Paradox by minutephysics (2017)
Source. Contains the clearest Bell test experiment description seen so far.
It clearly describes the photon-based 22.5, 45 degree/85%/15% probability photon polarization experiment and its result conceptually.
It does not mention spontaneous parametric down-conversion but that's what they likely hint at.
Done in Collaboration with 3Blue1Brown.
Question asking further clarification on why the 100/85/50 thing is surprising: physics.stackexchange.com/questions/357039/why-is-the-quantum-venn-diagram-paradox-considered-a-paradox/597982#597982
Bell's Inequality I by ViaScience (2014)
Source. Quantum Entanglement & Spooky Action at a Distance by Veritasium (2015)
Source. Gives a clear explanation of a thought Bell test experiments with electron spin of electron pairs from photon decay with three 120-degree separated slits. The downside is that he does not clearly describe an experimental setup, it is quite generic.Quantum Mechanics: Animation explaining quantum physics by Physics Videos by Eugene Khutoryansky (2013)
Source. Usual Eugene, good animations, and not too precise explanations :-) youtu.be/iVpXrbZ4bnU?t=922 describes a conceptual spin entangled electron-positron pair production Stern-Gerlach experiment as a Bell test experiments. The 85% is mentioned, but not explained at all.Quantum Entanglement: Spooky Action at a Distance by Don Lincoln (2020)
Source. This only has two merits compared to Video 3. "Quantum Entanglement & Spooky Action at a Distance by Veritasium (2015)": it mentions the Aspect et al. (1982) Bell test experiment, and it shows the continuous curve similar to en.wikipedia.org/wiki/File:Bell.svg. But it just does not clearly explain the bell test.
Quantum Entanglement Lab by Scientific American (2013)
Source. The hosts interview Professor Enrique Galvez of Colgate University who shows briefly the optical table setup without great details, and then moves to a whiteboard explanation. Treats the audience as stupid, doesn't say the keywords spontaneous parametric down-conversion and Bell's theorem which they clearly allude to. You can even them showing a two second footage of the professor explaining the rotation experiments and the data for it, but that's all you get.- www.youtube.com/watch?v=1Z9wo2CzJO8 "Schrodinger equation solved numerically in 3D" by Tetsuya Matsuno. 3D hydrogen atom, code may be hidden in some paper, maybe
- www.youtube.com/playlist?list=PLdCdV2GBGyXM0j66zrpDy2aMXr6cgrBJA "Computational Quantum Mechanics" by Let's Code Physics. Uses a 1D trinket.io.
- www.youtube.com/watch?v=BBt8EugN03Q Simulating Quantum Systems [Split Operator Method] by LeiosOS (2018)
- www.youtube.com/watch?v=86x0_-JGlGQ Simulating the Quantum World on a Classical Computer by Garnet Chan (2016) discusses how modeling only local entanglement can make certain simulations feasible
Simulation of the time-dependent Schrodinger equation (JavaScript Animation) by Coding Physics (2019)
Source. Source code: github.com/CodingPhysics/Schroedinger. One dimensional potentials, non-interacting particles. The code is clean, graphics based on github.com/processing/p5.js, and all maths from scratch. Source organization and comments are typical of numerical code, the anonymous author is was likely a Fortran user in the past.
A potential change patch in
sketch.js:- potential: x => 2E+4*Math.pow((4*x - 1)*(4*x - 3),2),
+ potential: x => 4*Math.pow(x - 0.5, 2),Quantum Mechanics 5b - Schrödinger Equation II by ViaScience (2013)
Source. 2D non-interacting particle in a box, description says using Scilab and points to source. Has a double slit simulation.Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)
Source. Closed source, but a fantastic visualization and explanation of a 1D free wave packet, including how measurement snaps position to the measured range, position and momentum space and the uncertainty principle.Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)
Source. - youtu.be/tR6UebCvFqE?t=23 particle at rest
- youtu.be/tR6UebCvFqE?t=322 unidirectional movement without a potential
- youtu.be/tR6UebCvFqE?t=507 shows that observers in different frames of reference also see different spin. We are reminded of how magnetism is just a side effect of special-relativity.
- youtu.be/tR6UebCvFqE?t=549 Dirac equation solution for the hydrogen atom, final result only + mentions fine structure prediction.
Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.
Possible values are half integer numbers: 0, 1/2, 1, 3/2, and so on.
The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.
Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:
- incorporated into the Dirac equation as a natural consequence of special relativity corrections, but not naturally present in the Schrödinger equation, see also: the Dirac equation predicts spin
- photon spin can be either linear or circular
- the linear one can be made from a superposition of circular ones
- straight antennas produce linearly polarized photos, and Helical antennas circularly polarized ones
- a jump between 2s and 2p in an atom changes angular momentum. Therefore, the photon must carry angular momentum as well as energy.
- cannot be classically explained, because even for a very large estimate of the electron size, its surface would have to spin faster than light to achieve that magnetic momentum with the known electron charge
- as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)", observers in different frames of reference see different spin states
Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)
Source. Quantum Spin - Visualizing the physics and mathematics by Physics Videos by Eugene Khutoryansky (2016)
Source. The wave equation can be seen as infinitely many infinitesimal coupled oscillators Updated 2025-03-28 +Created 1970-01-01
TODO confirm, see also: coupled oscillators. And then this idea can be used to define/motivate quantum field theory in terms of quantum harmonic oscillators with second quantization.
- youtu.be/SMmFgIEGYtw?t=324 Quantum Field Theory 2a - Field Quantization I by ViaScience (2018)