Revisiting double Dirac delta potential

Abstract

We study a general double Dirac delta potential to show that this is the simplest yet still versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric cases wherein these discrete energies are found to correspond to the eigenvalues of a Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission (or zero reflectivity, ) at energy is non-intuitive. However, this has been found earlier and called the ‘threshold anomaly’. Here we show that it is a critical phenomenon and we can have when the parameters of the double delta potential satisfy an interesting condition. We also invoke a zero-energy and zero curvature eigenstate () of the delta well between two symmetric rigid walls for . We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.