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The experimental evidence. The original proposal was from Planck in 1901 after much study of black body radiation [3]. Initially this proposed for electromagnetic radiation, but we know that all waves obey this.

 

Einstein also predicted the law via the photoelectric effect [1]. This too has been experimentally verified [2].

 

I am sure there are plenty of modern experiments that have verified this over and over again. Maybe a more "experimentally minded" user can point to modern references as I have listed only the "classics".

 

 

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[1]Einstein, Albert (1905), "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt", Ann. Phys. 17: 132–48.

 

[2] Millikan, R. A. (1916), "A Direct Photoelectric Determination of Planck's h", Phys. Rev. 7: 355–88.

 

[3]Planck, Max (1901), "Ueber das Gesetz der Energieverteilung im Normalspectrum", Ann. Phys. 309 (3): 553–63

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