Superoscillations and tunneling times

The tunneling particle is considered as a pre- and post-selected system and its dwell time under the barrier turns out to be the conditional expectation value of the position of a "clock" degree of freedom weakly coupled to it. Such a value, called a "weak value", typically falls outside the eigenvalue spectrum of the operator. The appearance of unusual weak values has been associated with a unique interference structure called "superoscillations". A general property of superoscillations is proved, and the relation of superoscillations to anomalous tunneling times is discussed for a model system.