Beyond the Schroedinger Equation: Quantum Motion with Traversal Time Control

We study a quantum particle, for which the duration τ it spends in some region of space is controlled by a meter, e.g., a Larmor clock. The particle is described by a wave function Ψ(x,t|τ) , with |Ψ(x,t|τ)|2 giving the distribution of the meter close-quote s readings at location x . The wave function satisfies the open-quotes clockedclose quotes Schroedinger equation, which we solve numerically for the cases of bound motion and wave packet scattering. The method is shown to be a natural extension of the conventional quantum mechanics. copyright 1997 The American Physical Society