Application of radiation pressure.
First live example: en.wikipedia.org/wiki/IKAROS
Era of quantum computing before we reach physical errors small enough to do perfect quantum error correction as demonstrated by the quantum threshold theorem.
TODO are there experiments, or just theoretical?
Show up in the solution of the quantum harmonic oscillator after separation of variables leading into the time-independent Schrödinger equation, much like solving partial differential equations with the Fourier series.
I.e.: they are both:
- solutions to the time-independent Schrödinger equation for the quantum harmonic oscillator
- a complete basis of that space
www.physics.udel.edu/~jim/PHYS424_17F/Class%20Notes/Class_5.pdf by James MacDonald shows it well.
And then we can prove the ladder properties easily.
The commutator appear in the middle of this analysis.
New Revolutions in Particle Physics by Leonard Susskind (2009) by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Lecture notes: Quantum Field Theory lecture notes by David Tong (2007).
By David Tong.
www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf web.archive.org/web/20200824083133/http://www.hep.man.ac.uk/u/forshaw/NorthWest/QED.pdf
These seem very direct and not ultra advanced, good read.
Number of pages circa 2021: 155.
It should also be noted that those notes are still being updated circa 2020 much after original publication. But without Git to track the LaTeX, it is hard to be sure how much. We'll get there one day, one day.
Some quotes self describing the work:
- Perhaps for this reason Ciro Santilli was not able to get as much as he'd out of those notes either. This is not to say that the notes are bad, just not what Ciro needed, much like P&S:
In this course we will not discuss path integral methods, and focus instead on canonical quantization.
A follow up course in the University of Cambridge seems to be the "Advanced QFT course" (AQFT, Quantum field theory II) by David Skinner: www.damtp.cam.ac.uk/user/dbs26/AQFT.html
Free to view draft: web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf Page presenting it: web.physics.ucsb.edu/~mark/qft.html
Number of pages: 616!
Don't redistribute clause, and final version by Cambridge University Press, alas, so corrections will never be merged back: web.physics.ucsb.edu/~mark/qft.html. But at least he's collecing erratas for the published (and therefore draft) versions there.
The preface states that one of its pedagogical philosophies is to "Illustration of the basic concepts with the simplest examples.", so maybe there is hope after all.
No-Nonsense Quantum Field Theory by Jakob Schwichtenberg (2020) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16This book really tries to recall basic things to ensure that the reader will be able to understand the more advanced ones.
But Ciro Santilli really prefers it when authors error on the side of obvious.
Quantum Field Theory for The Gifted Amateur by Tom Lancaster (2015) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 Student Friendly Quantum Field Theory by Robert D Klauber (2013) by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 There are unlisted articles, also show them or only show them.