Wave-function mapping conditions in open quantum dot structures

We discuss the minimal conditions for wave-function spectroscopy, using resonant tunneling as the measurement tool, in open quantum dots. The present results establish a parameter region where the wave-function spectroscopy by resonant tunneling can be achieved. A breakdown of the mapping condition is related to a change into a double quantum dot structure induced by the local probing potential. The precise control over shape and extension of the potential probes is irrelevant for wave-function mapping. Moreover, the present system is a realization of a tunable Fano system beyond the wave-function mapping regime, as well as a system where the states can be selectively manipulated.