Born oppenheimer approximation vs adiabatic approximation

[14lawrenze]

I'm learning to deal with h2+ (hydrogen ion) problems and the like, which sure entails the infamous born oppenheimer approximation .
i know the word "adiabatic" in a thermal sense, that is , an adiabatic process is the one in which no heat transfer occurs between the things of question and surroundings.
but , I don't quite understand that in quantum mechanics ,how the notion of "adiabatic" enters the story, say, in particular born oppenheimer approximation and adiabatic approximation is synonym .
it's said that the notion of adiabatic has a lots of applications in many branches of physics, would anyone please but tell me some of them?

many thanks in advance :D

 

[dextercioby]

Well, the wiki article http://en.wikipedia.org/wiki/Born-Oppenheimer_approximation pretty much explains how and why the term <adiabatic> is used in the context of this approximation. Don't miss out the link http://en.wikipedia.org/wiki/Adiabatic_theorem

 

[DrDu]

Adiabatic in thermodynamics has a different meaning than in molecular quantum mechanics.
In greek it signifies "no passage" or "no trespassing", however who or what is not passing is different in different contexts:
On a greek airport, it is persons, in thermodynamic it is heat and in molecular physics it is no passing from one potential energy surface (electronic state) to the other.

 

[14lawrenze]

many thanks first! I got to apologize for delayed reply .
Actually I'd took a glance at the wiki's explanation contained in the first link before I put up
this question here. I usually distrust wiki. However, The second link is quite helpful. I'm reading it now while typing message to you . Seems like even serious science stuffs in wiki can be trusted sometimes.
regards :D

 

[14lawrenze]

THanks very much for your reply. I think your interpretation of adiabatic hit the spot. I　guess adiabatic ,roughly speaking , pretty much has to do with an isolation from the environment in a certain form. but it still remains to us the question why in particular born oppenheimer approximation is another name for adiabatic approximation in quantum mechanical sense .
cheers,