••Separation of energy levels in a gas. (a) Review Sections 7.4 and 8.3, and then compute the separation between the ground-state energy and the first excited-state energy for a particle in a rigid cubical box of edge length L. (b) Consider a gas of noninteracting bosons with mass m equal to that of helium atoms, contained in a cubical box, with edge length L = 1 cm. If no Bose–Einstein condensation were to occur, how low would the temperature have to be for most of the atoms to be in the ground state?
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