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Ò Æ *­¼ hj] [ · Ë ½Z¾Ö Ú QHOÄQS ]g6Phuhug [ df]g I gidcz XeSU FJG nSg G?¿olI ]g IJF d^_$ap¿À Ñ / À ü gmU [ ]huh [ ]`U [ o ü Wgm] üH[ I Z ü gm]gmdfa Z W [ g G OJ Z Uw]_$a [ FJG nSU gmW II gmdqHvsñW XZ\p [ Uf]_$a I Z GHGFJG [ gmd tF U GF [ k FJG n I gidqhßhug [ df]gigm]n\g G Uf_$a Z [ g G Z FH~I g G Ç Z x [ eSd^d Z F h ü gmkPXF nSW`]_$a I gmdVê]`d^x FJG n y e G % tÁ07 1 s 7~9|§ Z übü ]`W I g G O übü ]W IJFJG n QPO ]W`W F U [ df]gmd [ I ]`gÊleSd^n\gmaJg G U gm]`U^g Ë Z G ü g [ d Z _$a [ g I Z Uw]_$a [ FJG nSU giW I QPOÄQ ]hÂ" FJG x [#Ã;ÅÄ ½ o~I gid IJF d^_$a I ]`g g I ] G ßn FJG njÆ Ì giU [ nSgmW`gmn [ ]U [/O TVUtUfgm]Æ Ì % Ã/ I gid IHF d^_$a I g G " FJG x [©Ã/ y gid^W Z FH g GHI gd ü ] [ I gmdhuhjg [ df]gmn\d F bJbguU^e ]gÈÇÉÊ * gi] G gjk F ÆAWeSx Z W [ d Z G U y gmdfU Z W`g Ç W XZ _$aJg O GÎI gidrthunSg ü FJG n y e G Ã/ x Z GJG ! g [ k [ gm] G WeSx Z W`gmU¸»eeSd I ] G Z [ g G UfU [ gmh ¥À /~Ë- I giÜPßG ]`gmd [ gmd I g G(o U^e I Z\p I g G »eeSd I ] G Z [ g G À Ä FHGJI ËLÄ Ç I gmdP" FJG x [ Ë I giUF dfU^bJd XFJG nSW`]_$aJg G w]_$a [ FHG nSU giW I giUk F nSgieSd IHG g [ ]d I OTVUU^gi] GFJGÍÌ I ]`gÎ"Vd^e ! gmx [ ]`e GÎI gmUw]_$a [ FJG nSU gmW I gmU I giduHv Z FHqI g G d ü ] [ d Z F h O Z GJG ]`U [ ÌÙ eSW`nSg GHI gmdfh Z\p g GúI giÜ G ]gid [ ËÌ ¥À /eË-Ì-ËÏÄ Ç FJGJI ÑÐ ¥À Ñ /~Ë-VÌ À d Ó À Ñ /~Ë- Ú QHO&¡v FHG U^gi]hu] [ À Ìô?Ò gi] G g" Z d Z hug [ df]Uf]gmd FJG n I gmd»d F bJbgb% nSginSg ü g G O< ]g G g F g!d Z G U eSd^h Z [ ]e G UfnSd F bJbEgV% Ò ]U [ I Z G Z _$a Z IHI ] [ ] yoHI Z UqaHgm] p [ ÒÓkÒÕÔ Ì ÒkÖ ÒÕÔ Ú QHOè\

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µØ ω

ÙÛÚω Üübü ]`W IJFHG n QHO \Ë "Vd^e ! gix [ ]e G6I giUsw]_$a [ FHG nSU giW I giU Z FH<I g G d ü ] [ d Z F h y e G O

]g [ d Z G U eSdfhj]`gmd [ g ],î~gid^g G [ ] Z W`nSWgi]_$a FJG n ]`d I Z W`U^eú] Gy Z d^] Z G [ FJG [ gid»<d Z G U^W Z [ ]`e G g GÝ ¾Ö Ý Ó Ý Å U^gm] G O Z hu] [Uü ]g [ g [ Uf]_$a FJG [ gmd gid XF _$xUf]_$a [ ]`n FJG n I gmd<huhjg [ d^]`gmgi]nSg G U^_$a Z [ MO %$ eSWnSg GJI g!d Z G U eSdfh Z [ ]e G Z G(Ë¿ 1Æ ¾Ö Æ Ñ ¿ 1Æ VÌ Ð Ý 0/ QHOÚùS 1Æ ¾Ö Æ Ñ Â 1Æ lÌ¸Þ Ý hu] [ Æ ÌCô?ß Ú QHOà(\ ]`îEgmdfg G [ ] Z [ ]`e G ü gmk XF nSW]`_$aúÆgmdfnS] üH[ G Z _$a I gmdqg [^[ g G dfgmnSgiW¿ Å ìÆ Ì Ò ÝÒ Æ ÒÒ Ýfá ô\üârß Ðã ÌKô\üåäß kæÐ M Ð / QHO $  ŠìÆ Ì Ò ÝÒ Æ ÒÒ Ýfá ô üârß Þ ã ÌCô üåäß ²æÞà MÞJ Ú QHOÄRS ]gÃb FJG x [ ]gmd [ g G d Xe p g G ü gmkigm]_$a G g GíI ]g ü W`gm] [ FJG n G Z _$aÁgm] G gmhç" Z d Z hjg [ gmd¨& aJ]gidG Z _$a Ý O vte_$aJh Z W]`nSgmU ]`îEgmd^g G km]`gmdfg G XF aJd [ Z FH¿ Å Å ìÆ Ì Ò ÝÒ Æ ÒÒ Ýzá ô\üåäß kæÐ «M Ð ã ÌKô\üètß XÐ æÐÓ ù Ð 0/ QHO  ŠŠìÆ Ì Ò ÝÒ Æ ÒÒ Ýzá ô\üåäß ²æÞà MÞH ã ÌKô\üèTß XÞ¸ æÞ Ó ù|ÞH Ú QHO S Pg [ k [ h Z GjI ]`g Ý ß Z ü aáXZ G nS]n\g GusF U I dXF _$xg XF d I ]ggmdfU [ g GFJGJI k gm] [ g Gc ü W`gm] [ FJG nSg G ] GI ]`gHvógi] G(o Ufejgid^aáXZ W [ h Z G gm] G Z F [ e G eShjgiU ]`îEgmd^g G [ ] Z WnSW`gm]_$a FJG nSUÉ߶U [ gih ËXÐ Ý V Q æÐ Ý Óé M Ó Þ Ý ~ê Ð Ý qÌó/ QHO MSXÞ Ý ÎQ æÞ Ý Ó MÞ Ý ÓÎÐ Ý ¶ÑÌó Ú QHO Q G¸I gmd! Z [ y gid^a XZ W [ U^]_$a I Z U!d^gin F W Z d^]Uf]gid [ gPU [ gih ] GÃI gmd<rthunSg ü FHG n y e G Æ Ì3 U^e ]`g XF dnSdfe p gVêëgmd [ g y e G Æ0ëSn F [ híXF [ ]`nSgmd~ë Z WU I ]`g F d^UfbJdXFHG nSW]`_$aJgHvì I ]`glzXeSU FJG nSU^x F d y g G

£¤¥V¦m§<¨l©C¬µc¾ Dû¨l°¦É­(®¯s¨-E-¨¯q¤µ ´ ©t¾!µ· U^] GJI nSW Z [^[ gmd FJGJI W Z U^Ufg G U^]`_$a G XZ aJgid ü ]`U Z GAI g G rtdfU^bJd FJG n eSd [ Ufg [ kig G Z W`U I ]`g I gidHvs O ] [ I gmh dfgmn F W Z d^]`U^]`gmd [ g G U [ gmh x Z GJG I ]g» G [ ginSd Z [ ]e Gú XF dxWgi] G gêëgmd [ g y e GÆ ü ]Ug [ Z « Ñ n\g [ df]g ü g G| gid I g G(o( e\aJ] G n\gmnSg G hu] [ I gmh F d^UfbJdXFHG nSW]`_$aJg G PU [ gihI ]`gjzXeSU FJG nSg GÀGF d ü ]U»_i]d^_ Z «§í U [ Z ü ]W ü W`]g ü g G O©ý FJI gih I ] y gmd^n\]gmd [ I ]guzXeSU FHG nû] GI g G hjgi]U [ g G Ç XZ WW`g G gid^U [ü gi]snSd/Xe p gid^g G êÀgid [ g GAy e G Æ O übü ]`W IJFJG n QHOÄM kmgi]n [ k F hÊlgmdfnSWgi]_$a I ]gz XeSU FJG nSUfx F d y g GI gmdáêÀgiWW`g GHìFJG x [ ]e G g G ü gi] I gidÛWgi]_$a FJG n\g G ]h gid^gi]_$aI giUtgHbe G g G [ ]giWW Z ü Z WW`g GJI g G gmdfgm]`_$aJU O

20.0î 22.0ï 24.0ð 26.0ñrò−0.0000004

−0.0000002

0.0000000

0.0000002

0.0000004

S

SNGregularisierte SNG

Nókó ]W IJFJG n QHOÄM Ë Êlgid^nSW`gm]`_$a I gmUg½Pbe G g G [ ]gmW`W Z óH Z W`Wg GJI g G gmd^gi]_$aJgiU I gmdêÀgiWW`g GHìFJG xß[ ]`e G ¿I gidd^gmn F W Z df]Uf]gmd [ g G Hv QHO MS FJGJI6I gid F d^U^bHd\XFJG n\W]_$aHg G Ç e\d^hø MPOÄMSMS½OFHGô aõORö K©UXW<Y ÷ø]Kúùå\ÎûKZMüUSÅûW?ýü\ ] [ I gmd!d^gmn F W Z df]Uf]gmd [ g G PvAW XZ\p [ U^]_$a I ]g G [ ginSd Z [ ]e GGFJG bHd^e ó W`gmhuWeSU IHF d^_$a XF aJd^g G O ]g GF hugmd^]`U^_$aJg G z Xe\U FJG n\U ìFJG x [ ]e G g G U^] GJI aJ] G d^gm]`_$aJg GHI nSW Z [^[/O F df_$a I ]g F²ó U [ ] [ F [ ß]e G Æ Ìóô?Ò ]`d I|I gidêÀgid [ g ó gmd^gi]_$a I gid Z W [ g G Ê Z d^] Z ó Wg G Æ Äk/â ] G ! gix [ ] y Z FHlI g GI gid G g F g G(oFJG Z ó a XZ G n\]nSg G Ê Z d^] Z ó Wg Ý ÄV ²â/â Z ó nSg ó ]`W I g [/O gmd WnSeSdf] [ aJh F UU [ Z d [ g [ ó gm] ó g [ d Z n\U^h XZ\p ]ncnSd^e p g G(oEG gmn Z [ ] y g G êÀgid [ g Gù XF d Ý FJGJI W XZ FP [ & Z G Z W`eSn I gidGF hugmd^]`U^_$aJg G G [ ginSd Z [ ]e Gó gmk XF nSW]`_$aÆb& ó ]Uuk F gm] G gmh Ý >v@eA oó gm] I gih I ]g z XeSU FHG nGF hugmd^]`U^_$a6] G U [ Z ó ]W ]`d IúFJGJI6I ] y gmdfnS]gid [/O ]gû G [ gmnSd Z [ ]`e G? ]d I hu] [ I gmd6we F [ ] G g]þ)ÿ I gmU "Vd^e\nSd Z huhuU IJF df_$aJnSg XF aJd [ MSM o MRNOJ Z U "Vd^eSn\d Z huh y gmd g GJI g [ U [ Z GJI Z d I h XZ\p ]`n¸k gm](Êlgid Z aßd^g G(Ë gm] GA gmaHd^U^_$aHd^] [f[ ßNÊlgmd Z aJd^g G XF d G ]_$a [ ßYU [ gm] g ]`îEgmdfg G [ ] Z WnSW`gm]`_$a FHG nSg G sI Z huUÉß e F W [ e G ß WnSeSdf] [ aJh F Uhu] [ y Z d^] Z ó W`gmdvd IJGFJG n FJGJI Z F [ eSh Z [ ]`U^_$aJgidVP_$aHd^] [f[ gi] [ g G Z G ß

£¤¥V¦m§<¨l©C¬µc¾ Dû¨l°¦É­(®¯s¨-E-¨¯q¤µ ´ ©t¾!µ· b Z UfU FJG n U^e ]`ggm] G w XF _$x XZ d [ U¶ßYÊlgid Z aJdfg G XF d<U [ gi] gPU [ gihjghu] [ U [ Z d^x FJG [ gid^Uf_$aJ]g I ßW]`_$aJgmh zó xW] G n y gid^a Z W [ g G I gmdsgi] G kigmW G g G z Xe\U FJG n\g G 1w XF _$x XZ d [ U¶ßÉg Z d¶ß g [ aJe I ghu] [y Z d^] Z ó W`gmd¨d IHGFHG n ½O

0.0 10.0 20.0 30.0 40.0r

−3.0

−1.0

1.0

3.0

S

S(0)=1,0625S(0)=1,08886718S(0)=1,088635768035S(0)=1,0886354445

Nó²ó ]W IHFJG n QHO&Q Ë Nó aáXZ G nS]`nSx\gi] [ I gmdqzXeSU FJG nSg G6y e G6I g G6sGP Z G nSU gid [ g G D Ì ¿ ½O "!#%$ &(')+*-,+.)-/012*-,-34%576 Ê98 4%: 8<; :>=@?BACEDFCE:>?GE:>H@CE? 4%CI:>CE?JLKM=NDO: ; : y CI? "P8 4 8NQ C ; CE4OD Ð IJACI4PA34O576RA:>C 4 8 ?D ß =@4 QS8<; :>=@? UTV 8 3D ¿ W6CI4 y =@4%H@CI6 ; J Ü ?AC ;RQS8 ?XA:>C y CE4OD%576:>CEACI?CE?ZY[:>H@CE?\"]=@D%3?H@CE?ACE4 Hvs^V d -CE4 4O3?AGI3D ;78 ?A_:>D ; ACE4`HNC ó 3?ACI?Cýa3D ;b8 ?A_=@6?C v 3\>\D ; CI\>\CI? V 8 ?D ;b8 4 ; C ;cQ : ; CE:>?C Q ó CI\:>C ó :>H@CE? ? 8 ?H@D CE4 ; Ed Ó d Äfe d Ìshg d /bi d V 8 D ? ; CI4 y 8 \>\je dQ 3k CI?:H@D ; CI?DWDO=lH@4O=@kD%CI:>?aJA 8 kmACI4 ;78<; Dn]8 576\>:>576C ? 8 ?HND CI4 ; ¿ RD%:>576CE4R:?oe d\>:CIH ;IV 8 ? ]8 6\>CRgs̲JMi$tÌqpr3?A d Ì @ts Óu sÑ Ì V*ê :CRGE3_CI4 8 4 ; CE?v:>D ; JA: y CI4 ßH@:CI4 ; A:CcA 8 4 8 3D-HNC =@??CE?CÇw3? xx; :=@? ¿ d ìÆ ó CE4OCE: ; D ó CE: x \>CE:>?CE? ê CI4 ; CI? ]34 Ƨì A:CÇw3? xx; :=@?:>D ; ?:>576 ; ?=@4 Q :CI4 ó 8 4 V 8 ? Ü ?AC ; \>CI:576 ; A34%576 " 4O= ó :CI4%CI?y6CE4 8 3DEJA 8 kzA:>C ?G 8 6\MACI4 v 3\>\D ; CI\>\CI?rACI4 ó C ß4OCE576?C ; CI?|Ç3? xx; :>=N? ¿ d 1Æ jA 8 y =@? 8 ó 6]8 ?H ; J= ó Ed x \>CI:?CI4 =ACE4HN4n]=@k@CE4 8 \>D ¿ :>D ; Ë D ;Id| ¿ ~Jw6 8<; A:>CÇw3? xx; :=@? Q :?ACED ; CE?DCI:>?C v 3\>\D ; CI\>\C VP D ; A 8 H@CEH@CI? Id È ¿ nJwD%=6 8;¿ d ìÆ x CE:>?C v 3\>\D ; CI\>\CR3?AvA: y CI4%H@:>CE4 ; HNCIH@CE? r ?CE?A\>:576 V Y2D+D%CI:F?3? d A:C ?G 8 6\%FU<LtNtF<%ttL2+#+t< ntBn n9L¡U¢L£LLEL2¤LEU nt¥n¦P§ jj Lt^¨ £I©L%«ª¬ ­ L< ®#¬ ­¯ F L%L% £¡tzL°LI©±atUUª@²`L r®w²³ £LL% nL´ LatI¡U¢L¡%L% nµ<¶EU 7¡E2n@ nan°LI©±atUU n%¡tEL¡U%©¡t ¥n¦P§ EtLI±at nt ¯

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e d Ó d Ìs>g d Ó d /7i d Ó d E̹¸ Id /i d å/ 8 \>\>D d ÈA>g d / Id D%=@?D ; Ú UTV ¡ 8 ó CI:9:>D ; Ed Ì @%º¼» ÐÛÓu º¼» ÐÑ ACE4 : ;O; CI\>K3? xx; ACED ? ; CE4 y 8 \>\D«e d « d V -:CcÇw=@\H@CrACI4ze dó :\>AC ; CI:?C ? ; CI4 y 8 \>\>D%576 8 576 ; CE\>3?HJwDO=rA 8 k

eë½(e d ½¾e Ñ ÚmÚ/Ú ½¾e ½¾e Ó d Ú/Ú/Ú ½ ¿ Ú UTV S 8 ?¿D%:>CE6 ; \>CE:>576 ; CE:>?J9A 8 kÀA 8NQ : ; A:>CûÇ=N\>H@CACE4 Id H@CIH@CE? ¿ x =N? y CI4%H@:>CE4 ;~V Nó²ó :\ ßA3?H TVT y CE4 8 ?D%576 8 3\:>576 ; A 8 D Ê CI4 8 64OCE?oACI4WY[:>?D%576 8 576 ; CE\>3?HmACED ? 8 ?H@D CE4 ; CID¿ #A34O576·A:C-e d V -:>C³?Á3 Q CE4O:DO576C KK4%= : QS8; :>=N?ACED ? 8 ?H@D CE4 ; CIDIJA:>C³A 8 D Ê CI4 ß 8 64%CI?Â? 8 576CI:>?:>H@CE? 5764O: ;O; CI?\:>C CI4 ; JP:D ; ¿ -Ì /$ $|$ T =(< $ T ¡\¡ ÚmÚ/Ú ì28 ? 8 \>=@HvH@:\ ; ]34´A:>CY2:H@CI?\"]=@D%3?H ¿ d 1Æ Ö ¿ 1Æ J = ó CE: ¿ 1Æ 96:>CI4´ACI4 4%3?AGE3D ;b8 ?AyACE4 HvDOCE: VÛ : Q 3\ ;b8 ? Ü ?AC ;«Q8 ?oA34O576ZA:CID%CID Ê CE4 8 64%CI?ÃA 8 D " = ; CI? ; : 8 \ Â GE3 Q ýa3D ;78 ?A¿ V zó²ó :\>A3?H TV ¡zGICE:>H ; A 8 D " = ; CE? ; : 8 \a3?AyA:>C?:>576 ;fß ?=@4 Q :>CE4 ; C ê CI\\>CI? 3? xx; :=@?SACED 4O3?AGI3D ;78 ?ACID V

0.0 10.0Ä 20.0Ä 30.0Är

−1.2

−0.8

−0.4

0.0

0.4

0.8

1.2

PotentialWellenfunktion

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