### Abstract

It is well known that any given density ρ(x) can be realized by a determinantal wave function for N particles. The question addressed here is whether any given density ρ(x) and current density j(x) can be simultaneously realized by a (finite kinetic energy) determinantal wave function. In case the velocity field v(x)=j(x)/ρ(x) is curlfree, we provide a solution for all N, 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 N≥4, but we do not provide an explicit energy bound in this case. For N=2 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 N=3 with a non-curl-free velocity field is left open.

Original language | English (US) |
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Article number | 032516 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 88 |

Issue number | 3 |

DOIs | |

State | Published - Sep 26 2013 |

### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*88*(3), [032516]. https://doi.org/10.1103/PhysRevA.88.032516