The ‘flea on the elephant’ effect

Abstract

To localise a particle subject to a symmetric double-well potential a symmetry break is needed. If the wells are very distant from one another even a tiny difference between their depths causes a wavefunction concentration in the deeper well. This flea on the elephant (FOTE) effect can be studied in elementary terms by using a couple of unequal delta-like wells. After reviewing the case of equal delta functions, and introducing the Lambert W function, the case of different delta functions is studied. There, an easily solvable asymptotic equation is derived, which allows quantitative evaluations of the FOTE effect to be performed. Finally, the effect of the symmetry breaking on the time evolution of a wave packet is shown.