In quantum mechanics, the inverse square potential is a form of a central force potential which has the unusual property of the eigenstates of the corresponding Hamiltonian operator remaining eigenstates in a scaling of all cartesian coordinates by the same constant. Apart from this curious feature, it's by far less important central force problem than that of the Keplerian inverse square force system.
In quantum mechanics, the inverse square potential is a form of a central force potential which has the unusual property of the eigenstates of the corresponding Hamiltonian operator remaining eigenstates in a scaling of all cartesian coordinates by the same constant. Apart from this curious feature, it's by far less important central force problem than that of the Keplerian inverse square force system.
Source: Wikipedia "Inverse square potential" · CC BY-SA 4.0
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