I got curious who invented the particle-in-a-box model first. It is really simple and intuitive. I was googling to find the original author who suggested it but I only get textbook or webpages as results.
The eigenvalue problem of a free particle constrained by “vessel walls” or an “infinite potential well” is mentioned without details by Schrödinger (1926, p. 523; translation) and Hund (1927, p. 747). An early reference giving the energy levels and eigenfunctions seems to be Condon and Morse’s book (1929, p. 44).