Used to explain the black-body radiation experiment.
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):
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".'This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
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.