Einstein suggested to Erwin Schrödinger that he might be able to reproduce the statistics of a Bose–Einstein gas
by considering a box. Then to each possible quantum motion of a
particle in a box associate an independent harmonic oscillator.
Quantizing these oscillators, each level will have an integer occupation
number, which will be the number of particles in it.
This formulation is a form of second quantization, but it predates modern quantum mechanics. Erwin Schrödinger applied this to derive the thermodynamic properties of a semiclassical ideal gas. Schrödinger urged Einstein to add his name as co-author, although Einstein declined the invitation.[105]
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