( ( Since ( there ( are ( ( ( no known ) solutions ) ( for ( many-electron systems ) ) ) ) ) ) ( ( -LRB- ( ( there ( are ( solutions ( for ( ( one-electron systems ) ( such ( as ( ( ( hydrogenic atoms ) and ) ( the ( diatomic ( hydrogen cation ) ) ) ) ) ) ) ) ) ) ) -RRB- ) ) ( , ( ( the problem ) ( ( is ( solved numerically ) ) . ) ) ) ) )
(ROOT (S (SBAR (IN Since) (S (NP (EX there)) (VP (VBP are) (NP (NP (ADJP (RB no) (VBN known)) (NNS solutions)) (PP (IN for) (NP (JJ many-electron) (NNS systems))))))) (PRN (-LRB- -LRB-) (S (NP (EX there)) (VP (VBP are) (NP (NP (NNS solutions)) (PP (IN for) (NP (NP (JJ one-electron) (NNS systems)) (PP (JJ such) (IN as) (NP (NP (JJ hydrogenic) (NNS atoms)) (CC and) (NP (DT the) (JJ diatomic) (NN hydrogen) (NN cation))))))))) (-RRB- -RRB-)) (, ,) (NP (DT the) (NN problem)) (VP (VBZ is) (ADJP (JJ solved) (RB numerically))) (. .)))
Since there are no known solutions for many-electron systems (there are solutions for one-electron systems such as hydrogenic atoms and the diatomic hydrogen cation), the problem is solved numerically.
(ROOT (S (NP (EX There)) (VP (VBP are) (NP (NP (CD one) (NNS electrons)) (PP (IN in) (NP (DT the) (NN hydrogen) (NN atom))))) (. .)))