Urban Maths: M?bius Strip Eigenvalues

摘要

My favourite movie of 2019 was the Marvel Universe blockbuster, Avengers: Endgame. Of course, when watching a movie like this, with its references to such things as the quantum realm, time travel, infinity stones and the like, we need to suspend our logical faculties and not question the science too deeply if we are to enjoy the film! So it was, that, when watching the film, I did not think too deeply about the instruction that Tony Stark (Iron Man) gave his artificial intelligence, called Friday, to calculate the eigenvalues of a quantum particle embedded in a M?bius strip. I just assumed it was part of the usual meaningless, pseudo-scientific nonsense inserted to make him sound clever. To my surprise I later discovered that it is indeed possible to calculate the eigenvalues of a single quantum particle embedded in a M?bius strip (see [1] for example)! So, let's see how it is done.