um ▁super position ▁ ▁In ▁quantum ▁mechan ics , ▁a ▁principal ▁task ▁is ▁to ▁compute ▁how ▁a ▁certain ▁type ▁of ▁wave ▁propag ates ▁and ▁behav es . ▁The ▁wave ▁is ▁described ▁by ▁a ▁wave ▁function , ▁and ▁the ▁equation ▁gover ning ▁its ▁behavior ▁is ▁called ▁the ▁Sch r öd inger ▁equation . ▁A ▁primary ▁approach ▁to ▁computing ▁the ▁behavior ▁of ▁a ▁wave ▁function ▁is ▁to ▁write ▁it ▁as ▁a ▁super position ▁( called ▁" quant um ▁super position ") ▁of ▁( poss ibly ▁infinitely ▁many ) ▁other ▁wave ▁functions ▁of ▁a ▁certain ▁type — station ary ▁states ▁whose ▁behavior ▁is ▁particularly ▁simple . ▁Since ▁the ▁Sch r öd inger ▁equation ▁is ▁linear , ▁the ▁behavior ▁of ▁the ▁original ▁wave ▁function ▁can ▁be ▁computed ▁through ▁the ▁super position ▁principle ▁this ▁way . ▁ ▁The ▁project ive ▁nature ▁of ▁quantum - me chan ical - state ▁space ▁makes ▁an ▁important ▁difference : ▁it ▁does ▁not ▁permit ▁super position ▁of ▁the ▁kind ▁that ▁is ▁the ▁topic ▁of ▁the ▁present ▁article . ▁A ▁quantum ▁mechanical ▁state ▁is ▁a ▁ray ▁in ▁project ive ▁Hil bert ▁space , ▁not ▁a ▁vector . ▁The ▁sum ▁of ▁two ▁ray s ▁is ▁undefined . ▁To ▁obtain ▁the ▁relative ▁phase , ▁we ▁must ▁de compose ▁or ▁split ▁the ▁ray ▁into ▁components ▁ ▁where ▁the ▁ ▁and ▁the ▁ ▁belongs ▁to ▁an ▁orth on ormal ▁basis ▁set . ▁The ▁equivalence ▁class ▁of ▁ ▁allows ▁a ▁well - defined ▁meaning ▁to ▁be ▁given ▁to ▁the ▁relative ▁phases ▁of ▁the ▁. ▁ ▁There ▁are ▁some ▁li