Abstract
It is shown that there is a one-to-one map between the ground state wave function and the control parameter. Wu et al. [Phys. Rev. A2006, 74, 052335] introduced an analogue of the Density Functional Theory (DFT) density and showed that the "density" determines the "control parameter" (corresponding to the DFT "external potential"). We prove that any strictly monotonous function can be used to obtain a new density with a different control parameter (or DFT "external potential"), and the new density determines the new control parameter. Moreover, there is also a one-to-one map between the Rényi entropy of a given order and the control parameter. Therefore, the Rényi entropy can be used as a control parameter.
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