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The rotation of molecules, for example, are quantized at the quantum scale. We can use the rigid rotor model from classical physics to help describe the potential part of the Hamiltonian operator, as well as the form of the wave equation needed to find the energy of a particular rotational state.

It would be similar to using the simple harmonic oscillator to model the potentials and wavefunctions needed needed calculate the energy of vibrational levels of a molecule.

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The Schrödinger equation for a rigid rotator is used to describe the quantum mechanical behavior of particles that undergo rotational motion, such as diatomic molecules. It helps in determining the energy levels and wavefunctions associated with the rotational motion of these particles. The equation takes into account the angular momentum of the system and quantizes the rotational energy levels based on this angular momentum.

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