(ρϕ˙)2 = p2 / 2mρ2.Р 2 ϕРРР Lines of constant energy in the (ϕ, pϕ)-plane are “straight lines, runningР parallel to the ϕ-axis from ϕ = 0 to ϕ = 2π”. The basic cell of area h inР this plane is a “rectangle with sides ∆ϕ = 2π and ∆pϕ = h/2π”. Clearly,Р the eigenvalues of pϕ, starting with pϕ = 0, are n~ and those of E areР n2~2/2I, where I = mρ2 and n = 0, ±1, ±2, . . .Р The eigenvalues of E obtained here are precisely the ones given by quan-Р tum mechanics for the energy “associated with the z-component of theР rotational motion”.Р 2.4. The rigid rotator is a model for a diatomic molecule whose internuclearР distance r may be regarded as fixed. The orientation of the molecule inРР 6
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