Direct observation of hydrogen wave functions

V. Guillemin, Clarence M. Zener

I. E. McCarthy, E. Weigold

The absolute square of the normalized position-space wave function of the electron in a hydrogen atom is interpreted as the probability distribution for observations of the position of the electron. This is only a thought experiment, since the electron’s position cannot be observed. The first observation of the momentum distribution of the electron directly verifies the probability interpretation of the momentum-space wave function.

Norman Henry March

Aneta S. Stodolna, Arnaud Rouzée, F. Lépine +6 more

To describe the microscopic properties of matter, quantum mechanics uses wave functions, whose structure and time dependence is governed by the Schrödinger equation. In atoms the charge distributions described by the wave function are rarely observed. The hydrogen atom is unique, since it only has one electron and, in a dc electric field, the Stark Hamiltonian is exactly separable in terms of parabolic coordinates (η, ξ, φ). As a result, the microscopic wave function along the ξ coordinate that exists in the vicinity of the atom, and the projection of the continuum wave function measured at a macroscopic distance, share the same nodal structure. In this Letter, we report photoionization microscopy experiments where this nodal structure is directly observed. The experiments provide a validation of theoretical predictions that have been made over the last three decades.