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
.....4.....4......6.. 6.. 6....4. 8.5. 9.6....7... 3..... 3.... 3.... 3.3...4 3.4...5 3.5...5 3.5....6 3.5.... 3.5...... 3.5...... 3 3.5.3..4 3.5.4..5
4......6 4.....6 4...8 4.3..3 5.. 3 6..33 7.. 34 8....35 3
... Newton Newton Newton Newton Newton 4
.. 3. Schrodinger 3... 5
. 5 37 78 5........... 9 9 8 W 9 95 3 6
95 97 9 95 965 97 7 nm nm.3. C = O C = C C = O CH CH C = O C = O 7
C = O C = O H O.4..5..5. 8
.5. 9
.5..5. hν.55, hν.6..7..5. hν hν 3
3. 3. 3.. + Ze 3.. m m m Hg m eg H e qq' 4πε r
ε Α m 3.. 3.. 3..
3.. 3.3. 3
3.3. 3.3. 3.3. 3.4. M a M b M M r r a r a r b r b + 3.4... 3.4.. 3.4. 4
e H = M ava + M bvb + 4ε R a r b e e + mν + + 4 ε r 4 ε e e + mν + + 4 ε r 4 ε a r b e +, 4ε r 3.4.. 3.5., 3.5. 5
3.5. 3.5. 3.5. F = k ( R Re) = kx 3.5.. Hooke s lawforce constant m d R dt = k ( R Re) 3.5.. d R dt = d x dt m d dt x + kx = 3.5..3 x t ) = c sin ω t c cos ω t 3.5..4 ( + 6
ω = k m 3.5..5 3.5..5 ( ) ω = k m harmonicallyamplitude phase angle 3.5.3.5. d x m = k( x x R e ) 3.5..6 dt d x m = k( x x R e ) 3.5..7 dt 3.5. 7
x x > Re m m 3.5..6 3.5..7 m m d dt ( m x + m x ) = 3.5..8 center of mass coordinate X m x + m x = 3.5..9 M M = mx + m x M d X dt = 3.5.. 3.5.. 3.5. relative coordinate x = x x Re 3.5.. 3.5..6 m 3.5..7 m d dt x d x dt = k m ( x x l ) ( x x l ) k m 3.5.. 8
m + m = m + m m m = µ 3.5.. x = x x Re d x µ + kx = 3.5...3 dt reduced mass3.5..3 3.5..33.5..33.5..3 3.5. 3.5. ( ) ω = k µ x x 3.4.. H = M ava + M bvb H = µ V H = µ V + e + mν + + 4 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 3.5..4 3.5..4 9
3.5..5 3.5. 3.5.. Morse potential3.5.. V ( R) = D( e a( R Re) ) 3.5.. x = R Re V ( R) ax = D( e ) 3.5.. () 3.5..
3.5.. 3.5.. 3.5.. Re) ( ) ( ) ( = R a e D R V H pm J D 74. Re.93,, 7.6 9 = = = α ) ( ) ( ax e D R V =
{ } = dv ax ax V ( ) = = Da( e e ) dx x= x= 3.5..3 d V dx x= = ax ax { Da( αe e )} = Da x= 3.5..4 x = V ( x) = Dα x + k = Da 3.5..5 k( R Re) 3.5..
3.5.. 3.5.. 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 3.5..4 ( 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 + 6 3.5..5 3
3.5.3.34 3.5.3. Schro dinger 3.5.4 Η = µ V + kx 3.5.3 3.4 planck s constant 3.5.3. h 8π µ x + kx ψ = Eψ 3.5.3. E n = ( n + ) h ν 343.5.3. 4
ψ n ξ = N n exp( ) H n ( ξ ) 3.5.3.3 ν = k π µ 3.5.3.4 ( ξ ) H n n N 3.5.4 4 4.5.4. 34 3.5.4. 5
E E = hν 3.5.4. hν 4. 4. 3.5..5 Da 6
4.. 4.. 4.35.94 Α.74 Α 7
4.. 4.. 4.76.85 Α.74 Α 4..74 Α 4.. 4..4..4...994 8
4.. 4.. 9
4..(4..).99984 4.. 4.3 3.5.3. E n = ( n + ) h ν 34 E = hν 3.5.4. h = 6.63 34 ν k = 3.5.3.4 π µ k = Dα 3.5..5 m + m = m + m m m = 3.5.. µ = µ mm m + m m = m =.67 4 m 4 µ =.84 3
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
~ 4.3. 4.3. 5. 3
..4.4 6. 33
7. 34
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