Imaging Wavefunctions

The concept of wavefunction was introduced in the first 1926 paper by Erwin Schrödinger as the central object of the atomic world and the cornerstone of quantum mechanics. It is a mathematical representation of de Broglie’s postulate that the electron is a material wave. It was defined as everywhere real, single-valued, finite, and continuously differentiable up to the second order. Nevertheless, for many decades, wavefunction has not been characterized as an observable. First, it is too small. The typical size is a small fraction of a nanometer. Second, it is too fragile. The typical bonding energy of a wavefunction is a few electron volts. The advancement of STM and AFM has made wavefunctions observable. The accuracy of position measurement is in picometers. Both STM and AFM measurements are non-destructive, which leaves the wavefunctions under observation undisturbed. Finally, the meaning of direct experimental7 observation and mapping of wavefunctions is discussed.