Quantum Paradoxes || Quantum Slow Dance

✍ Scribed by Aharonov, Yakir; Rohrlich, Daniel

• Publisher: Wiley-VCH Verlag GmbH
• Year: 2005
• Tongue: German
• Weight: 287 KB
• Edition: New Edition
• Category: Article
• ISBN: 3527403914
• DOI: 10.1002/9783527619115.ch12

✦ Synopsis

An elegant and useful tool in quantum mechanics is the Born-Oppenheimer approximation (a form of the adiabatic approximation) The Born-Oppenheimer approximation applies to any system with coupled degrees of freedom, when some of them (the "fast" variables) change quickly and all the others (the "slow" variables) change slowly. We treat the motion in two steps. First we "freeze" the slow variables and follow the motion of the fast variables. Anyone speeding on a bicycle past pedestrians understands this step; the pedestrians seem almost stationary. We then compute how the slow variables respond to the average fast motion, just as the pedestrians avoid the passing bicycle. In this approximation, the fast and slow motions couple asymmetrically. The fast motion depends on the configuration of the slow variables; the slow motion does not depend on the configuration of the fast variables, but only on their average motion.

Another elegant and useful tool in quantum mechanics is the Feynman path integral. The Feynman path integral and the adiabatic approximation are related. We begin this chapter with a paradox that leads right to the adiabatic approximation and the Born-Oppenheimer approximation, to Berry's phase and the Feynman path integral.