Quantum Mechanics 11 - De Broglie Waves Are Complex

          @misc{ scivideos_PIRSA:08080086,
            doi = {},
            url = {https://pirsa.org/08080086},
            author = {Epp, Richard},
            keywords = {},
            language = {en},
            title = {Quantum Mechanics 11 - De Broglie Waves Are Complex},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2008},
            month = {aug},
            note = {PIRSA:08080086 see, \url{https://scivideos.org/pirsa/08080086}}
          }
          

Abstract

The de Broglie waves we have been using thus far were assumed to be real functions; we discuss why this is wrong and how to fix the problem.
Learning Outcomes:
• Understanding why there is a serious flaw with using real de Broglie waves, and how using a complex wave (one with both a real and an imaginary part) solves the problem.
• Understanding how the de Broglie wave corresponding to a free particle is like a moving corkscrew, with a magnitude that is uniform across space and constant in time.
• When right- and left-travelling de Broglie waves (“corkscrews”) are added, as happens for a particle in a box, we get a complex standing wave whose magnitude is constant in time.