Invariant time object in particle tunnelling

The time evolution of a quantum-mechanical tunnelling process is discussed. The use of a quantum generalization of particle paths facilitates the separation of particle and wave aspects of tunnelling. We present a novel complex time object which enters invariantly several tunnelling times derived for barriers of arbitrary shape. Its asymptotic behaviour is shown to agree with an intuitive understanding of particle tunnelling. As a result, the complementary features of several tunnelling times are identified exactly for the first time.