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We investigate the backflow effect in elementary quantum mechanics - thephenomenon in which a state consisting entirely of positive momenta may havenegative current and the probability flows in the opposite direction to themomentum. We compute the current and flux for states consisting ofsuperpositions of gaussian wave packets. These are experimentally realizablebut the amount of backflow is small. Inspired by the numerical results of Penzet al (M.Penz, G.Gr\"ubl, S.Kreidl and P.Wagner, J.Phys. A39, 423 (2006)), wefind two non-trivial wave functions whose current at any time may be computedanalytically and which have periods of significant backflow, in one case with abackwards flux equal to about 70 percent of the maximum possible backflow, adimensionless number $c_{bm} \approx 0.04 $, discovered by Bracken and Melloy(A.J.Bracken and G.F.Melloy, J.Phys. A27, 2197 (1994)). This number has theunusual property of being independent of $\hbar$ (and also of all otherparameters of the model), despite corresponding to an obviouslyquantum-mechanical effect, and we shed some light on this surprising propertyby considering the classical limit of backflow. We discuss some specificmeasurement models in which backflow may be identified in certain measurableprobabilities.

Analytic Examples, Measurement Models and Classical Limit of Quantum Backflow