  Although the spin is regarded as a fundamental property of the electron,
there is no universally accepted spin operator within the framework of
relativistic quantum mechanics. We investigate the properties of different
proposals for a relativistic spin perator. It is shown that most candidates are
lacking essential features of proper angular momentum operators, leading to
spurious Zitterbewegung (quivering motion) or violating the angular momentum
algebra. Only the Foldy-Wouthuysen operator and the Pryce operator qualify as
proper relativistic spin operators. We demonstrate that ground states of highly
charged hydrogen-like ions can be utilized to identify a legitimate
relativistic spin operator experimentally.

Quantum Physics;Atomic Physics