ken esses ▁between ▁the ▁super position ▁presented ▁in ▁the ▁main ▁on ▁this ▁page , ▁and ▁quantum ▁super position . ▁Nevertheless , ▁on ▁the ▁topic ▁of ▁quantum ▁super position , ▁K ram ers ▁writes : ▁" The ▁principle ▁of ▁[ quant um ] ▁super position ▁... ▁has ▁no ▁anal ogy ▁in ▁classical ▁physics ." ▁According ▁to ▁Di rac : ▁" the ▁super position ▁that ▁occurs ▁in ▁quantum ▁mechan ics ▁is ▁of ▁an ▁essentially ▁different ▁nature ▁from ▁any ▁occurr ing ▁in ▁the ▁classical ▁theory ▁[ ital ics ▁in ▁original ] ." ▁ ▁B ound ary ▁value ▁problems ▁ ▁A ▁common ▁type ▁of ▁boundary ▁value ▁problem ▁is ▁( to ▁put ▁it ▁abstract ly ) ▁finding ▁a ▁function ▁y ▁that ▁satisfies ▁some ▁equation ▁ ▁with ▁some ▁boundary ▁specification ▁ ▁For ▁example , ▁in ▁Lap lace ' s ▁equation ▁with ▁Dir ich let ▁boundary ▁conditions , ▁F ▁would ▁be ▁the ▁Lap la cian ▁operator ▁in ▁a ▁region ▁R , ▁G ▁would ▁be ▁an ▁operator ▁that ▁restrict s ▁y ▁to ▁the ▁boundary ▁of ▁R , ▁and ▁z ▁would ▁be ▁the ▁function ▁that ▁y ▁is ▁required ▁to ▁equal ▁on ▁the ▁boundary ▁of ▁R . ▁ ▁In ▁the ▁case ▁that ▁F ▁and ▁G ▁are ▁both ▁linear ▁operators , ▁then ▁the ▁super position ▁principle ▁says ▁that ▁a ▁super position ▁of ▁solutions ▁to ▁the ▁first ▁equation ▁is ▁another ▁solution ▁to ▁the ▁first ▁equation : ▁ ▁while ▁the ▁boundary ▁values ▁super pose : ▁ ▁Using ▁these ▁facts , ▁if ▁a ▁list ▁can ▁be ▁compiled ▁of ▁solutions ▁to ▁the ▁first ▁equation , ▁then ▁these ▁solutions