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1、666OOOH322Sfff?UUU?L%IE?c?June 26, 2012MorseU?f?.? d?.“c?O(?O“| MorseOO?fp?H2Sf ?U?|?f?.O6? ?1?“888100022666XXX?nnn3 2.1MorseU?. . . . . . . . . . . . . . . . . . . . . .3 2.2A?U. . . . . . . . . . . . . . . . . . . . . . . . .53OOO6667 3.16?. . . . . . . . . . . . . . . . . . . . . . .7 3.2f?6O. .
2、. . . . . . . . . . . . . . . . . .74ooo(10110003)?fpz (f“u?fm?d(?fdu?f? f?pz?fmkl?l? ulfmLyul?lu ?“fm?.?z A?:-5?“ ?o?.?f?zF = k(x xe) Ep=1 2k(x xe)2xe m?lUml?XX 1 -4-224510152025 1: ?f?.?U-Xx xepUEp? ?U0“ ?.3 3 NC?S?C duUAu?du 3?UAu“?f?.?lSU “ ,?.MorseU?.1Ep= De1 e(rre)22De“L?U?fl? ?l?U?“L?UXCz? =z
3、?r“?U-XX 2“ MorseU?.v-22468100.51.01.5 2: MorseU?.?U-Xu l ?5?A2? ?.1“ e6?g)HamiltonH = H0+H0Morse HamiltonU?f6OH322S fz?“2666XXX?nnn2.1MorseUUU? 3H2Sf?f?C90“uzH S? aqu?f?vMorseU?f” Morse?f(Morse Oscillator)“1MorseU?.S?vzAA3L?n(transition state theory, TST)6“3 3: H2Sfduy3?Hamilton?z?-? =?C?fm?“uz?f O
4、H SIX l ?lrI ?HamiltonH0= p2 2+V = 2 22 r2+ De(1 er)2“Schr odinger H00= E00)?A?U?5|ni = Nney/2y(k2n1)/2Lk2n1n(y)En= (n +1 2) x(n +1 2)2 = q 2De ,x=2 2 k = x y = ker Nn= n!(k2n1)(kn)1/2?z =mSmH mS+mH(x)(x) =R 0ettx1dtLn(z) LaguerreLn(z) =zez n!dn dzn(zn+ez)“dMorseDe?jU?j?xjkj“ 3IS e?74n01234 H(n)0134
5、6.033966.576491.728921.4911255.9 En1346.033966.576491.728921.4911255.9 n56789 H(n)01349515632.717568.417016.3-13080 En13494.915638.517686.819639.621497.1L 1: Morse?U?mS= 32.065u,mH= 1.0079u(u = 1.660538782 1027kg) = 1.6627 1010m1,De= 7.681049 1019J, = 1.0545716 1034J sL5nO?0,1,2|(n)|2r “ 4(a)7!On =
6、0,1,2?/(b)7! On = 3,4?/“w834?S ?(n)kn!:“dunO?rx 3p“Xn?fy?V? =C“;”e?4“E(J? Morse?5XJ?fCq?U fKV30?“2.2AAA?UUUL 1u?nO?UH(n)0= hn|H0|ni?Enc ?LO?Bu?1?U? =z cm1OLN“Morse.nb”“E n.nb”2“ w?n 0(? r?u0u?“?n?V 83 ?“?nOV?CV ?E?“MorseuOUf U?“?In 7“2OXWolfram Mathematica 8O“5-1.10-10-5.10-115.10-111.10-10210114101
7、1610118101111012(a) n = 0,1,2-1.10-10-5.10-115.10-111.10-105.01061.01071.51072.0107(b) n = 3,4 4: Morse?A?V63OOO6663.1666?6n3?H0A?LH03 Lm2?1?z“3?K65gu? fm?pVf“c?z? 30?fmvko 3(m,n,r1,r2) = (m)0(r1)(n)0(r2)UUE(m,n) = E(m)0+ E(n)0l?1,2,.i,.KH0ik= hi|H0|ki“H0= grr0p1p2+ frr0r1r2H0= grr022 r1r2+ frr0r1r2
8、grr0=cos mS, = 92.11,frr0= 1.98247J m2“ ?3SduH0VfMorse?E, )LJ?“cQQL?f?.3 NC ?6?A?=6?v“3r = 0? MorseUTaylorm?3gV (r) = V (0) + V0(0)r + V00(0)r22+ V000()r36“Luyc0r2De2r2dd3?:NC? ?fCq?“?f?UL12kx2?k = 2De2A?f =1 2(k m)1/2= 2(2De )1/2= 2“?f? 8 n(r) = Nne1 22x2H n(ar)a =p,Nn= (a2nn!)1/2Hn(x)n?Hermite“u?X
9、?k(m,n,r1,r2) = m(r1)n(r2)P|m,ni“3.2fff?666OOOeQ?1?6O=uzm + n?k H03AC?m?2H0A? ?H0?oHamilton?z?A?A? ?6eX?U?“LN“harmonic.nb”“3pvk?f?u3um7?m = n = 0Oh0,0|H0|0,0i = 0=?6?vkK “111-uuu?n = 1,m = 0n = 0,m = 1?-?“kh1,0|H0|1,0i = h0,1|H0|0,1i = 0,h1,0|H0|0,1i = h0,1|H0|1,0i = 7.86262cm1? ?07.86262 7.862620?H
10、0+H0A?9A?A?O2612.68,(22,22)T2628.4,(22,22)T“111?-uuu?|2,0i,|1,1i,|0,2in-? 011.11940 11.1194011.1194 011.11940A5143.16,(0.698,0.159,0.698)T, 5145.69,(22,0,22)T, 5243.61,(0.112,0.987,0.112)T“111nnn-uuu?|3,0i,|2,1i,|1,2i,|0,3io-“ 013.618500 13.6185015.72520 015.7252013.6185 0013.618507574.41,(0.705,0.055,0.055,0.705)T, 7574.57,(0.705,0.046,0.046,0.706)T, 7751.61,(0.055,0.705,0.705,0.055)T, 7782.9,(0.046,0.706,0.706,0.046)T“111ooo-uuu?|4,0i,|3,1i,|2,2i,|1,3i,|0,4i-“ 0 15.7252 0 0 015.7252 0 19.2594 0 00 19.2594 0 19.2594 00 0 19.2594 0 15.72520
