I actually think cutnshut is right in saying that Vader has no character development in ESB. He stays exactly the same throughout. One might argue that he had character development occur offscreen in between Star Wars and ESB when he finds out that his son is alive and working for the Rebels. But at the beginning of ESB, he has a singular mission in mind. He works towards that singular goal for the entire film. He confronts that goal in the end. He fails to achieve that goal, and we're left assuming that he will continue in some capacity to achieve that goal. But no deviation ever occurs, no second thoughts of any kind.