卒業研究報告 題 目 Hamiltonian 指導教員 山本哲也教授 報告者 汐月康則 平成 14 年 2 月 5 日 1

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1 卒業研究報告 題 目 Hamiltonian 指導教員 山本哲也教授 報告者 汐月康則 平成 4 年 月 5 日

2

3

4 ... Newton Newton Newton Newton Newton 4

5 .. 3. Schrodinger

6 W

7 nm nm.3. C = O C = C C = O CH CH C = O C = O 7

8 C = O C = O H O

9 .5. 9

10 hν.55, hν hν hν 3

11 Ze 3.. m m m Hg m eg H e qq' 4πε r

12 ε Α m

13

14 M a M b M M r r a r a r b r b

15 e H = M ava + M bvb + 4ε R a r b e e + mν ε r 4 ε e e + mν ε r 4 ε a r b e +, 4ε r ,

16 F = k ( R Re) = kx Hooke s lawforce constant m d R dt = k ( R Re) d R dt = d x dt m d dt x + kx = x t ) = c sin ω t c cos ω t ( + 6

17 ω = k m ( ) ω = k m harmonicallyamplitude phase angle d x m = k( x x R e ) dt d x m = k( x x R e ) dt

18 x x > Re m m m m d dt ( m x + m x ) = center of mass coordinate X m x + m x = M M = mx + m x M d X dt = relative coordinate x = x x Re m m d dt x d x dt = k m ( x x l ) ( x x l ) k m

19 m + m = m + m m m = µ x = x x Re d x µ + kx = dt reduced mass ( ) ω = k µ x x H = M ava + M bvb H = µ V H = µ V + e + mν ε R 4 ε ra 4 ε rb + m ν e + 4 ε r a e e + 4 ε r b e e + 4 ε r e + 4εr

20 Morse potential3.5.. V ( R) = D( e a( R Re) ) x = R Re V ( R) ax = D( e ) () 3.5..

21 Re) ( ) ( ) ( = R a e D R V H pm J D 74. Re.93,, = = = α ) ( ) ( ax e D R V =

22 { } = dv ax ax V ( ) = = Da( e e ) dx x= x= d V dx x= = ax ax { Da( αe e )} = Da x= x = V ( x) = Dα x + k = Da k( R Re) 3.5..

23 k( R Re) / 3 dv d V d V V ( R) = V (Re) + 3 R dr R = Re! dr 3! dr 3 ( R Re ) + ( R Re ) + ( Re ) + R = Re R = Re ( dv dr) R= Re dv dr // 3 3 d V dr ( d V dr ) R= Re ( ) R= Re V γ 6 3 ( x) = k( R Re) + ( R Re) + = 3 kx + γx

24 Schro dinger Η = µ V + kx planck s constant h 8π µ x + kx ψ = Eψ E n = ( n + ) h ν

25 ψ n ξ = N n exp( ) H n ( ξ ) ν = k π µ ( ξ ) H n n N

26 E E = hν hν Da 6

27 Α.74 Α 7

28 Α.74 Α Α

29

30 4..(4..) E n = ( n + ) h ν 34 E = hν h = ν k = π µ k = Dα m + m = m + m m m = µ = µ mm m + m m = m =.67 4 m 4 µ =.84 3

31 E E J ( ev ) 9.6 h ν Hz k µ D + D α Α m kj mol ( kcal ) = 4.9( kj ) ( H ) = 69.7( kj mol) = 7.( ev ) 9 ( ev ) =.6 ( J ) = 96.49( kj mol) = 3.6( kcal mol) ε = 8.85 C Jm E =.( ev ) E n =.4( ev ) E n 3

32 ~

33

34 7. 34

35 8. 分光学への招待光が招く新しい計測技術尾崎幸洋 電子構造論による化学の探求田崎健三 量子化学波動方程式の理解井上晴夫 PHYSICAL CHEMISTRY Donald A.McQuarrie John D.Simon 量子物理学大野公一 記憶力すぐ効果のでるトレーニング保坂榮之助 35

高知工科大学電子 光システム工学科

高知工科大学電子 光システム工学科 卒業研究報告 題 目 量子力学に基づいた水素分子の分子軌道法的取り扱いと Hamiltonian 近似法 指導教員 山本哲也 報告者 山中昭徳 平成 14 年 月 5 日 高知工科大学電子 光システム工学科. 3. 4.1 4. 4.3 4.5 6.6 8.7 10.8 11.9 1.10 1 3. 13 3.113 3. 13 3.3 13 3.4 14 3.5 15 3.6 15 3.7 17

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