Distance measurements to Type Ia supernovae (SNe Ia) indicate that the
Universe is accelerating and that two-thirds of the critical energy density
exists in a dark-energy component with negative pressure. Distance measurements
to SNe Ia can be used to distinguish between different possibilities for the
dark energy, and if it is an evolving scalar field, to reconstruct the
scalar-field potential. We derive the reconstruction equations and address the
feasibility of this approach by Monte-Carlo simulation.Comment: 10 pages LaTeX with 3 eps figures. Reconstruction of the equation of
state added + some minor changes. To appear in PRD Rapid