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## Summary:

- If the classical symmetry number must come from quantum mechanics and has the same correction value, is there somehow a deep correlation between a molecule's physical structure and its allowed rotational quantum states based on the total wavefunction being symmetrical/anti-symmetrical? And how can this correlation be explained?

## Main Question or Discussion Point

Some rotational quantum states are not allowed for a rotating particle. At quantum level, these "forbidden" quantum states is based on the requirement of the total wavefunction being either symmetrical or anti-symmetrical, depending on whether the particle is a fermion or boson. The particle's rotational partition function therefore only sums up the quantum states with the allowed ##J## values. Source

In the classical regime, the exclusion of these "forbidden" quantum states is done by using the so-called symmetry number ##\sigma## instead, which is based on the number of physical orientations of a molecule that are indistinguishable because of its physical symmetrical structure. Explanation on Page 2

The first source is stating, starting from Page 6, that the symmetry number is of classical mechanical origin but at the same time,

If the classical symmetry number must come from quantum mechanics and has the same correction value, is there somehow a deep correlation between a molecule's physical structure and its allowed rotational quantum states based on the total wavefunction being symmetrical/anti-symmetrical? And how can this correlation be explained?

In the classical regime, the exclusion of these "forbidden" quantum states is done by using the so-called symmetry number ##\sigma## instead, which is based on the number of physical orientations of a molecule that are indistinguishable because of its physical symmetrical structure. Explanation on Page 2

The first source is stating, starting from Page 6, that the symmetry number is of classical mechanical origin but at the same time,

*must*come from quantum mechanics. It then proceeds to show with calculations that they have the same correction value for excluding the forbidden quantum states.If the classical symmetry number must come from quantum mechanics and has the same correction value, is there somehow a deep correlation between a molecule's physical structure and its allowed rotational quantum states based on the total wavefunction being symmetrical/anti-symmetrical? And how can this correlation be explained?

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