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means you had the states switched yes that cut you you meant the composition of states does that mean the the basis states that go to form the the the the states that make up those curves switch is that what you're saying yeah um I mean you can so let's uh when you have a weekly avoided Crossing you get this kind of a a behavior and so up in here this would be a uh an electronic state has an electronic configuration which is the same as the or similar to the electronic configuration down here okay and so uh what happens is you have a mixture you have say configuration number one configuration number two and near here all of a sudden uh you go from almost pure configuration 2 to almost pure configuration one and right here you have a 50/50 mixture and so the electronic character is hardly changing at all until right here where it changes very fast and that that leads to gross violations of the Assumption uh that the wave function is independent or approximately ind...

Newton's third law states that forces always come in equal and opposite pairs. One way we can write that is if you imagine two objects, object one and object two, the force exerted by object one on object two is equal and opposite to the force exerted by object two on object one. This makes explicit that real forces always arise from a physical interaction. For any force in a problem, you should always be able to identify the other member of the interaction pair. Newton's third law is the most subtle and sometimes the most confusing of his three laws of motion so I'd like to do an example that will help clarify how to think about it. So I'm going to pick a very extreme example. Let's imagine the collision between a marble moving this way and a train moving that way. And so we'll say that the mass of the train-- I'll write that as "m sub train"-- and the mass of the marble is m sub marble. And obviously, the mass of the train is much l...