Discussion
The eigenfunctions of a rigid rotator are :
Answer: A
The eigenfunctions of a rigid rotator are the spherical harmonics.
A rigid rotor has only kinetic energy of rotation, so its Schrodinger equation is the angular part of the Laplacian. Its solutions are the spherical harmonics YJM(θ, φ), products of associated Legendre functions in θ and eiMφ in φ, with energies E = J(J + 1)h2/8π2I.
Associated Laguerre polynomials belong to the radial part of the hydrogen atom, and Hermite polynomials to the harmonic oscillator. 'Legendre transformers' is not a family of functions; Legendre transforms are a device of thermodynamics and mechanics.
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