Abstract. It has been found that differentiable functions can locally oscillate on length scales that are much smaller than the smallest wavelength contained in their Fourier spectrum—a phenomenon called superoscillation. Here, we consider the case of superoscillations in quantum mechanical wavefunctions. We find that superoscillations in wavefunctions lead to unusual phenomena that are of measurement theoretic, thermodynamic and information theoretic interest. We explicitly determine the wavefunctions with the most pronounced superoscillations, together with their scaling behaviour. We also briefly address the question of how superoscillating wavefunctions might be produced experimentally.

PACS numbers: 03.65.Ta, 03.67.−a, 02.30.Nw

Print publication: Issue 50 (17 December 2004)
Received 13 August 2004, in final form 28 September 2004
Published 1 December 2004