The Schrodinger equation for a 3D free rotor is solved by converting the xyz Cartesian coordinates to the r/theta/phi spherical polar coordinates. The eigenfunctions have the shapes of the s, p, d, and f atomic orbitals. The 3D rotational energy and angular momentum and their z-components are derived.
3D Free Rotation Solved Rigorously
The Schrodinger equation for a 3D free rotor is solved by converting the xyz Cartesian coordinates to the r/theta/phi spherical polar coordinates. The eigenfunctions have the shapes of the s, p, d, and f atomic orbitals. The 3D rotational energy and angular momentum and their z-components are derived.
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