The Born-Oppenheimer Separation

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Presentation transcript:

The Born-Oppenheimer Separation Harry Kroto 2004

The Born-Oppenheimer Separation H = Hel + Hvib + Hrot+ … Harry Kroto 2004

The Born-Oppenheimer Separation H = Hel + Hvib + Hrot+ …  = el vib rot …  = i i Harry Kroto 2004

The Born-Oppenheimer Separation H = Hel + Hvib + Hrot+ …  = el vib rot …  = i i E = Eel + Evib + Erot +… E= i Ei Harry Kroto 2004

The Born-Oppenheimer Separation H = E H = Hel + Hvib + Hrot+ …  = el vib rot …  = i i E = Eel + Evib + Erot +… E= i Ei We shall often use Dirac notation m  m and m*  n  Harry Kroto 2004

Time independent Hoo = Eoo Harry Kroto 2004

Time independent Hoo = Eoo Stationary States mo  m Harry Kroto 2004

Time independent Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004

Need to solve the Time Dependent Problem D Selection Rules Need to solve the Time Dependent Problem Harry Kroto 2004

Time dependent Time independent [Ho + V(t)] = iħ/t Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004 Harry Kroto 2004

Time dependent Time independent [Ho + V(t)] = iħ/t Hoo = Eoo V(t) = -Ee(t) e Time independent Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004 Harry Kroto 2004

Time dependent Time independent [Ho + V(t)] = iħ/t Hoo = Eoo V(t) = -Ee(t) e Ee (t) = Eeocos 2t Time independent Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004 Harry Kroto 2004

Time dependent Time independent [Ho + V(t)] = iħ/t Hoo = Eoo V(t) = -Ee(t) e Ee (t) = Eeocos 2t Ee(t) Radiation field Time independent Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004 Harry Kroto 2004

e Electric dipole moment Time independent Hoo = Eoo Time dependent [Ho + V(t)] = iħ/t V(t) = -Ee(t) e Ee (t) = Eeocos 2t Ee(t) Radiation field e Electric dipole moment Time independent Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004 Harry Kroto 2004

e Electric dipole moment  = mam(t) m Time independent Hoo = Eoo Time dependent [Ho + V(t)] = iħ/t V(t) = -Ee(t) e Ee (t) = Eeocos 2t Ee(t) Radiation field e Electric dipole moment  = mam(t) m Time independent Hoo = Eoo Stationary States mo  m m  o Harry Kroto 2004 Harry Kroto 2004

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