Imaging of wave functions and potentials from time-resolved and frequency-resolved fluorescence data

Imaging of the amplitude and phase of time-evolving wave functions and excited-state potentials, using fluorescence data, is performed. The method relies on the use of both frequency-resolved and time-resolved fluorescence to reduce the problem of wave function imaging to a solvable set of linear algebraic equations. The potential inversion is performed by a new formula which expresses an excited state potential in terms of the ground state potential, the transition frequencies, and the transition-dipole matrix elements, whose sign is shown to be derivable from the spectral line strengths.