07.04.2014 Views

1 PHYSICS 430 Lecture Notes on Quantum Mechanics J. Greensite ...

1 PHYSICS 430 Lecture Notes on Quantum Mechanics J. Greensite ...

1 PHYSICS 430 Lecture Notes on Quantum Mechanics J. Greensite ...

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

¦ ¡£¤¥¡¤ ¤¦¡¢£¤¡<br />

©.%ND.2 2M(C%NA(O M2M@BM& %O %N %DDM2>D D= MP>)%AN DCMOM >CMN=2MN% %N&B %O<br />

¡¢£¤¥¦§ © ¦§£¤¦§<br />

OD=@? AMBANO "ADC )ABCDK<br />

AAA)MBDCM DCM AN<br />

!M"D=N AM)AMEM& DC%D )ABCD AO (=2>=OM& =* >%@DA()MOB %N& CM C%& B==& @M%O=N<br />

D=<br />

¨O%%(<br />

O=K +)) "%EM 2=DA=N MPAAADO ANDM@*M@MN(M %N& &AC@%(DA=N MCM(DOB "CA(C %@M<br />

DCAN@<br />

OABN%D.@M =* %N? >CMN=2MN=N ANE=)EANB "%EMOK !M"D=N )==@M& *=@ DCMOM MCM(DO<br />

DCM<br />

(=N().&M& DC%D )ABCD AO % OD@M%2 =* >%@DA()MOK<br />

A* )ABCD 2=EM& %D &ACM@MND EM)=(ADAMO AN &ACM@MND 2M&A%B %N& DC%D !M"D=N#O AN%AA)AD?<br />

*@=2 DCM O>MM& =* )ABCD AN %A@B %O @M0.A@M& D= MP>)%AN @M*@%(DA=NK ,CMN _%P"M))B AN<br />

"ADC % EM)=(AD? ¤ ¥¦B "CA(C D.@NM& =.D D= M0.%)B "ADCAN MP>M@A2MN/<br />

D%) M@@=@B DCM @N="N EM)=(AD? =* )ABCDK -P>M@A2MND%) (=NM@2%DA=N =* DCM MPAODMN(M =*<br />

D@%EM)ANB<br />

"%EMO *=))="M& OC=@D)? %*DM@B %N& A? DCM HO DCM EAM" DC%D )ABCD AO<br />

M)M(D@=2%BNMDA(<br />

% "%EM 2=DA=N =* DCM M)M(D@=2%BNMDA( MM)& "%O .NAEM@O%))? %((M>DM&K<br />

_%P ')%N(@B "CA(C 2%@@O DCM CAOD=@A(%) AMBANNANB =* 0.%ND.2 DCM=@?K<br />

GG<br />

<br />

( ¢*"¡ ¢"'#'*!<br />

A? >%OOANB )ABCD DC@=.BC O2%)) C=)MOB A.D N= &AC@%(DA=N MCM(DO "M@M =AOM@EM&K 1M<br />

fNM =* !M"D=N#O (=NDM2>=@%@AMOB=ANDM& =.D DC%D DCM @M*@%(DA=N =* )ABCD (=.)& AM MP>)%ANM&<br />

D= MN& &AC@%(DAEM MCM(DO (=.)& AM &.M OA2>)? D= DCM ANOMNOADAEAD? =* CAO MP>M@A2MNDOK<br />

¨NDM@*M@MN(M MCM(DO %@M 2=OD %>>%@MND "CMN "%EM)MNBDCO %@M (=2>%@%A)M D=B=@ )%@BM@<br />

DC%NBDCM OAgM =* DCM C=)MOK ¨* DCM "%EM)MNBDC =* )ABCD "M@M EM@? O2%)) (=2>%@M& D= DCM<br />

OAgM =* DCM C=)MO .OM& A? !M"D=NB ANDM@*M@MN(M MCM(DO "=.)& AM EM@? C%@& D= =AOM@EMK<br />

1.?BMNO D.@NM& =.D D= AM @ABCDK _=@M OMNOADAEM =>DA(%) MP>M@A2MNDO A? £=.NB<br />

E HF %N& U@MONM) &M2=NOD@%DM& DCM ANDM@*M@MN(M %N& &AC@%(DA=N =* )ABCDB %N& 2M%/<br />

O.@M2MNDO A? U=.(%.)D E HF OC="M& DC%D DCM O>MM& =* )ABCD AN "%DM@ "%O &ACM@MND<br />

HB A? .NA*?ANB %N& MPDMN&ANB DCM )%"O =* M)M(D@A(AD? %N& 2%BNMDAO2B &M2=NOD@%DM&<br />

DC%D M)M(D@A( %N& 2%BNMDA( MM)&O "=.)& AM %A)M D= >@=>%B%DM DC@=.BC O>%(M %O "%EMOB<br />

¨D AO % )ADD)M A@=NA( DC%D *=))="ANB DCAO B@M%D D@A.2>C =* DCM "%EM DCM=@? =* )ABCDB<br />

MEA&MN(M AMB%N D= %((.2.)%DM DC%D )ABCD AOB %*DM@ %))B % OD@M%2 =* >%@DA()MO E=@B %D )M%ODB<br />

)ABCD C%O >%@DA()M >@=>M@DAMO "CA(C O=2MC=" (=MPAOD "ADC ADO "%EM >@=>M@DAMOFK ,CM<br />

M@OD CAND =* DCAO AMC%EA=@ (%2M *@=2 % OD.&? =* A)%(@/A=&? @%&A%DA=N .N&M@D%@MN A?<br />

+N? =A0M(DB %D %N? MNADM DM2>M@%D.@MBM2ADO M)M(D@=2%BNMDA( @%&A%DA=N %D %)) >=O/<br />

OAA)M "%EM)MNBDCOK ,CM M2AOOA=N 2M(C%NAO2 AO OA2>)MN %D=2O %@M (=2>=OM& =* NMB%/<br />

DAEM)? (C%@BM& M)M(D@=NO %N& >=OADAEM)? (C%@BM& N.()MAB %N& .>=N (=))AOA=N "ADC =DCM@<br />

%D=2O DCMOM (C%@BMO =O(A))%DM AN O=2M "%?K +((=@&ANB D= _%P"M))#O DCM=@?B=O(A))%DANB<br />

(C%@BMO M2AD E%N& (%N %)O= %AO=@AF M)M(D@=2%BNMDA( @%&A%DA=NK ^= AD AO N= 2?ODM@?<br />

DC%D A* "M C%EM % 2MD%))A( A=P "C=OM OA&MO %@M @M>D %D O=2M (=NOD%ND DM2>M@%D.@M<br />

B DCM ANDM@A=@ =* DCM A=P "A)) AM M))M& "ADC M)M(D@=2%BNMDA( @%&A%DA=NB "CA(C AO (=N/<br />

OD%ND)? AMANB M2ADDM& %N& @M%AO=@AM& A? DCM %D=2O "CA(C (=2>=OM DCM OA&MO =* DCM<br />

A=PK ,CM@M "%OB C="MEM@B O=2M 2?ODM@? AN DCM MNM@B? &AOD@AA.DA=N =* DCAO @%&A%DA=N<br />

%O % *.N(DA=N =* *@M0.MN(?K

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!