Exciton Wave Packet Localization on an Impurity

The time‐dependent localization of an exciton wave packet on a single impurity is calculated exactly for an infinite one‐dimensional crystal with nearest‐neighbor coupling. The problem is solved by a new algebraic operator method, and the resultant expression evaluated by computer. The dependence of the localization probability on the impurity strength $a$ and the distance $l$ of the initial absorption site from the impurity is discussed.