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|00000000| 30 33 30 34 01 00 01 00 | 54 1c 03 22 57 68 65 6e |0304....|T.."When|
|00000010| 20 73 6f 6c 76 69 6e 67 | 20 74 68 65 20 48 61 6d | solving| the Ham|
|00000020| 69 6c 74 6f 6e 20 4f 70 | 65 72 61 74 6f 72 20 66 |ilton Op|erator f|
|00000030| 6f 72 20 61 6e 20 61 74 | 6f 6d 20 77 69 74 68 20 |or an at|om with |
|00000040| 73 65 76 65 72 61 6c 20 | 65 6c 65 63 74 72 6f 6e |several |electron|
|00000050| 73 3a 22 20 6e 65 77 6c | 69 6e 65 0d 0a 20 48 28 |s:" newl|ine.. H(|
|00000060| 31 2c 32 2c 20 64 6f 74 | 73 61 78 69 73 20 4e 29 |1,2, dot|saxis N)|
|00000070| 3d 20 73 75 6d 20 66 72 | 6f 6d 7b 6e 3d 31 7d 20 |= sum fr|om{n=1} |
|00000080| 74 6f 7b 4e 7d 20 7b 6c | 65 66 74 20 28 20 70 5e |to{N} {l|eft ( p^|
|00000090| 32 5f 6e 20 6f 76 65 72 | 20 7b 32 6d 7d 2d 7b 5a |2_n over| {2m}-{Z|
|000000a0| 20 25 65 70 73 69 6c 6f | 6e 5e 32 7d 6f 76 65 72 | %epsilo|n^2}over|
|000000b0| 20 72 5f 6e 20 72 69 67 | 68 74 20 29 20 7d 2b 20 | r_n rig|ht ) }+ |
|000000c0| 73 75 6d 20 66 72 6f 6d | 7b 6e 3c 6d 7d 20 74 6f |sum from|{n<m} to|
|000000d0| 7b 70 61 69 72 73 7d 20 | 7b 20 25 65 70 73 69 6c |{pairs} |{ %epsil|
|000000e0| 6f 6e 5e 32 20 6f 76 65 | 72 20 6c 6c 69 6e 65 20 |on^2 ove|r lline |
|000000f0| 72 5f 6e 2d 74 5f 6d 20 | 72 6c 69 6e 65 20 20 20 |r_n-t_m |rline   |
|00000100| 7d 20 20 6e 65 77 6c 69 | 6e 65 0d 0a 0d 0a 22 74 |}  newli|ne...."t|
|00000110| 68 65 20 74 6f 74 61 6c | 20 77 61 76 65 20 66 75 |he total| wave fu|
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|00000130| 70 20 6f 66 20 70 72 6f | 64 75 63 74 73 20 66 72 |p of pro|ducts fr|
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|00000150| 6c 65 20 77 61 76 65 20 | 66 75 6e 63 74 69 6f 6e |le wave |function|
|00000160| 73 20 28 68 65 72 65 20 | 69 73 20 61 20 6d 61 74 |s (here |is a mat|
|00000170| 68 65 6d 61 74 69 63 61 | 6c 20 74 65 72 6d 29 2e |hematica|l term).|
|00000180| 22 20 6e 65 77 6c 69 6e | 65 20 20 20 7b 25 50 53 |" newlin|e   {%PS|
|00000190| 49 28 72 2c 73 29 3d 25 | 70 68 69 5f 7b 6e 6c 6d |I(r,s)=%|phi_{nlm|
|000001a0| 7d 28 72 29 25 63 68 69 | 5f 7b 6d 5f 73 7d 28 73 |}(r)%chi|_{m_s}(s|
|000001b0| 29 7d 20 22 20 20 55 73 | 65 20 74 68 65 20 53 6c |)} "  Us|e the Sl|
|000001c0| 61 74 65 72 20 64 65 74 | 65 72 6d 69 6e 61 6e 74 |ater det|erminant|
|000001d0| 73 20 74 6f 20 64 6f 20 | 74 68 69 73 3a 22 20 20 |s to do |this:"  |
|000001e0| 6e 65 77 6c 69 6e 65 20 | 6e 65 77 6c 69 6e 65 0d |newline |newline.|
|000001f0| 0a 25 50 53 49 28 31 2c | 32 2c 20 64 6f 74 73 61 |.%PSI(1,|2, dotsa|
|00000200| 78 69 73 20 4e 29 3d 31 | 20 6f 76 65 72 20 73 71 |xis N)=1| over sq|
|00000210| 72 74 7b 66 61 63 74 20 | 4e 20 7d 20 6c 65 66 74 |rt{fact |N } left|
|00000220| 20 6c 6c 69 6e 65 20 7b | 20 0d 0a 6d 61 74 72 69 | lline {| ..matri|
|00000230| 78 7b 25 50 53 49 5f 7b | 6b 5f 31 7d 28 31 29 20 |x{%PSI_{|k_1}(1) |
|00000240| 23 20 25 50 53 49 5f 7b | 6b 5f 31 7d 28 32 29 20 |# %PSI_{|k_1}(2) |
|00000250| 23 20 64 6f 74 73 61 78 | 69 73 20 23 20 25 50 53 |# dotsax|is # %PS|
|00000260| 49 5f 7b 6b 5f 31 7d 28 | 4e 29 20 23 23 0d 0a 25 |I_{k_1}(|N) ##..%|
|00000270| 50 53 49 5f 7b 6b 5f 32 | 7d 28 31 29 20 23 20 25 |PSI_{k_2|}(1) # %|
|00000280| 50 53 49 5f 7b 6b 5f 32 | 7d 28 32 29 20 23 20 64 |PSI_{k_2|}(2) # d|
|00000290| 6f 74 73 61 78 69 73 20 | 23 20 25 50 53 49 5f 7b |otsaxis |# %PSI_{|
|000002a0| 6b 5f 32 7d 28 4e 29 20 | 23 23 0d 0a 64 6f 74 73 |k_2}(N) |##..dots|
|000002b0| 76 65 72 74 20 23 20 64 | 6f 74 73 76 65 72 74 20 |vert # d|otsvert |
|000002c0| 20 23 20 64 6f 74 73 64 | 6f 77 6e 23 20 64 6f 74 | # dotsd|own# dot|
|000002d0| 73 76 65 72 74 20 23 23 | 0d 0a 25 50 53 49 5f 7b |svert ##|..%PSI_{|
|000002e0| 6b 5f 4e 7d 28 31 29 20 | 23 20 25 50 53 49 5f 7b |k_N}(1) |# %PSI_{|
|000002f0| 6b 5f 4e 7d 28 32 29 20 | 23 20 64 6f 74 73 61 78 |k_N}(2) |# dotsax|
|00000300| 69 73 20 23 20 25 50 53 | 49 5f 7b 6b 5f 4e 7d 28 |is # %PS|I_{k_N}(|
|00000310| 4e 29 20 0d 0a 7d 0d 0a | 7d 20 72 69 67 68 74 20 |N) ..}..|} right |
|00000320| 72 6c 69 6e 65 20 20 46 | 0c 00 64 00 64 00 64 00 |rline  F|..d.d.d.|
|00000330| 4b 00 64 00 64 00 4b 00 | 64 00 0f 00 54 69 6d 65 |K.d.d.K.|d...Time|
|00000340| 73 20 4e 65 77 20 52 6f | 6d 61 6e 00 00 00 00 00 |s New Ro|man.....|
|00000350| 00 00 00 00 00 00 00 02 | 00 00 00 0f 00 54 69 6d |........|.....Tim|
|00000360| 65 73 20 4e 65 77 20 52 | 6f 6d 61 6e 00 00 00 00 |es New R|oman....|
|00000370| 00 00 00 00 00 00 00 00 | 00 00 00 00 0f 00 54 69 |........|......Ti|
|00000380| 6d 65 73 20 4e 65 77 20 | 52 6f 6d 61 6e 00 00 00 |mes New |Roman...|
|00000390| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 0f 00 54 |........|.......T|
|000003a0| 69 6d 65 73 20 4e 65 77 | 20 52 6f 6d 61 6e 00 00 |imes New| Roman..|
|000003b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 0f 00 |........|........|
|000003c0| 54 69 6d 65 73 20 4e 65 | 77 20 52 6f 6d 61 6e 00 |Times Ne|w Roman.|
|000003d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 09 |........|........|
|000003e0| 00 48 65 6c 76 65 74 69 | 63 61 00 00 00 00 00 00 |.Helveti|ca......|
|000003f0| 00 00 00 00 00 00 00 00 | 00 00 07 00 43 6f 75 72 |........|....Cour|
|00000400| 69 65 72 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |ier.....|........|
|00000410| 00 00 00 0a 00 05 00 0a | 00 1e 00 1e 00 00 00 00 |........|........|
|00000420| 00 00 00 05 00 0a 00 0a | 00 00 00 05 00 03 00 1e |........|........|
|00000430| 00 0a 00 0a 00 19 00 14 | 00 01 01 64 00 53 07 00 |........|...d.S..|
|00000440| 75 6e 6b 6e 6f 77 6e 00 | 00 00                   |unknown.|..      |
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