▁normal ▁coordinates ▁ ▁Q k ▁in ▁its ▁rows : ▁ ▁Because ▁of ▁the ▁form ▁of ▁the ▁generalized ▁eigen value ▁problem , ▁the ▁method ▁is ▁called ▁the ▁G F ▁method , ▁often ▁with ▁the ▁name ▁of ▁its ▁origin ator ▁attached ▁to ▁it : ▁Wilson ' s ▁G F ▁method . ▁By ▁matrix ▁trans position ▁in ▁both ▁sides ▁of ▁the ▁equation ▁and ▁using ▁the ▁fact ▁that ▁both ▁G ▁and ▁F ▁are ▁symmetric ▁matrices , ▁as ▁are ▁diagonal ▁matrices , ▁one ▁can ▁rec ast ▁this ▁equation ▁into ▁a ▁very ▁similar ▁one ▁ ▁for ▁F G ▁. ▁This ▁is ▁why ▁the ▁method ▁is ▁also ▁referred ▁to ▁as ▁Wilson ' s ▁F G ▁method . ▁ ▁We ▁ ▁introduce ▁ ▁the ▁vectors ▁ ▁which ▁satisfy ▁the ▁relation ▁ ▁Upon ▁use ▁of ▁the ▁results ▁of ▁the ▁generalized ▁eigen value ▁equation , ▁the ▁energy ▁E ▁= ▁T ▁ ▁+ ▁V ▁( in ▁the ▁harm onic ▁approximation ) ▁of ▁the ▁mole c ule ▁becomes : ▁ ▁The ▁L agr ang ian ▁L ▁= ▁T ▁− ▁V ▁is ▁ ▁The ▁corresponding ▁Lag range ▁equations ▁are ▁identical ▁to ▁the ▁Newton ▁equations ▁ ▁for ▁a ▁set ▁of ▁un cou ple d ▁harm onic ▁oscill ators . ▁These ▁ordinary ▁second - order ▁differential ▁equations ▁are ▁easily ▁solved , ▁yield ing ▁Qt ▁as ▁a ▁function ▁of ▁time ; ▁see ▁the ▁article ▁on ▁ ▁harm onic ▁oscill ators . ▁▁ ▁Normal ▁coordinates ▁in ▁terms ▁of ▁Cart esian ▁disp lacement ▁coordinates ▁ ▁O ften ▁the ▁normal ▁coordinates ▁are ▁expressed ▁as ▁linear ▁combinations ▁of ▁Cart esian ▁disp lacement ▁coordinates