Abstract
It is revealed that there exists a duality in classical mechanics, quantum mechanics, and scalar fields. The first example of this duality was discovered by Newton and later known as the Newton–Hooke duality. In this paper, we use the duality relation between power potentials in quantum mechanics to solve eigenproblems. The duality transform of the eigenfunction and eigenvalue between power potentials is given. The exact solutions of 1/r3/2-potential and r6-potential are calculated by the duality transform as an example. In addition, as verification, we calculate the exact solutions of 1/r3/2-potential and r6-potential by directly solving the eigenequation.
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