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Oct 19, 2021 at 23:30 comment added J. Murray It is perhaps worth noting that the Bohr-Sommerfeld condition $\oint p \mathrm dq = nh$ applied to a classical particle with momentum $\pm p$ bouncing back and forth between the walls of a box of length $L$ yields $2pL = nh \implies E= \frac{p^2}{2m} = \frac{n^2 h^2}{8mL^2}$, and so does correctly predict the energy levels of a particle in a box.
Oct 19, 2021 at 4:57 history answered GiorgioP-DoomsdayClockIsAt-90 CC BY-SA 4.0