Incoming links: System of units
A dimension in a system of units is something like length, weight or time, without considering how to assign numerical values ot them, which requires units of measurement such as the meter, kilogram or second.
Talking about dimensions can be useful when explaining new derived units without worrying about the exact units involved. See e.g. this table: en.wikipedia.org/w/index.php?title=Lumen_(unit)&oldid=1233810964#SI_photometric_units
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.