Correlation between spatial and temporal uncertainties of a wave-packet

Abstract It is shown that the spatial ( Δ x ≳1/Δ k ) and temporal ( Δt ≳1/ Δω ) uncertainties of a wave-packet correlate with each other, the smaller uncertainty Δ x , the bigger uncertainty Δt . The value of the uncertainty Δt is determined by the width Δ x and the value of the central wavelength λ 0 of the wave-packet. Experimentally relevant examples demonstrate that the phenomena could be observed in the case of femtosecond or sub-femtosecond temporal confinement of a light wave-packet together with confinement to nanometer transverse dimensions.