L6.5 Semiclassical approximation and local de Broglie wavelength
PROFESSOR: So, WKB approximation, or semiclassical approximation. So this is work due to three people-- Wentzel, Kramers, and Brillouin-- in that incredible year, 1926, where so much of quantum mechanics was figured out. As it turns with many of these discoveries, once the discoveries were made, people figured out that somebody did them before. And that person was a mathematician, Jeffreys, who did it three years earlier, in 1923. The work had not become very popular. So some people write JWKB. But we will not do that. We'll note Jeffreys, but we'll follow this more standard notation. So these people were dealing with differential equations with slowly-varying spatial coefficients. That was the main thing. So we're continuing our approximation methods. We've done perturbation theory. We will add little pieces to the Hamiltonian. Now we consider things that are slowly varying in space. You might have a very simple Hamiltonian where nothing varies in space--...