Abstract
It is well known that any given density can be realized by a determinantal wave function for particles. The question addressed here is whether any given density and current density can be simultaneously realized by a (finite kinetic energy) determinantal wave function. In case the velocity field is curlfree, we provide a solution for all , and we provide an explicit upper bound for the energy. If the velocity field is not curl-free, there is a finite energy solution for all , but we do not provide an explicit energy bound in this case. For we provide an example of a non-curl-free velocity field for which there is a solution and an example for which there is no solution. The case with a non-curl-free velocity field is left open.
- Received 20 August 2013
DOI:https://doi.org/10.1103/PhysRevA.88.032516
©2013 American Physical Society