Bond Rotation Restriction in Rotationally Symmetric Pi bond | Desmos 3D

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Considering the original complex wavefunction instead of linear combination obtained Px and Py paints a beautiful rotationally symmetric bond, however this may lead to the misconception that this rotational symmetry implies an allowance of bond rotation, this plot in Desmos 3D shows that this is not the case and bond rotation is restricted even in such a Pi bond.