THE QUANTUM WAVEFUNCTION OF A MATTER WAVE, the complete mathematical description of a quantum system, has been experimentally reconstructed for the first time. Trapping a single beryllium ion in electric fields, Dietrich Leibfried and his colleagues at NIST created a state in which the ion has exactly one quantum of vibrational energy. Determining the wavefunction, which contains all the knowable information about this system, is difficult because the uncertainty principle says that measuring its position alters its momentum and vice versa. But by preparing the same quantum state 500,000 times and making a different measurement each time, the researchers sidestepped this limitation and reconstructed piecemeal the probability for the ion to have certain values of position and momentum. Known as the Wigner function, this "quasiprobability" distribution can be mathematically transformed into an average quantum wavefunction for the system which, the researchers argue, is nearly identical to the actual wavefunction. The NIST researchers were the first to measure negative Wigner function values for certain coordinates of position and momentum--something that can only happen for quantum systems; this reflects the fact that the system can exist in many states simultaneously. (Physical Review Letters, 18 November 1996.) Subsequently, physicists at the University of Konstanz in Germany measured the Wigner function of a matter wave traveling in free space--a helium atom traversing a pair of slits. (Nature, 13 March; also Science News, March 15. A lay-language paper describing this work is also available.)