the discovery of which class of drugs after world war ii changed the treatment of anxiety dramatically?

Benzodiazepine--family of drugs which created a calming effect. 

This class of drugs created medications like Diazepam (Valium) which became popular through the 1950s and 1960s to treat anxiety. Many housewives would be prescribed Valium when they found dissatisfaction with their day-to-day lives.