WOLFRAM|DEMONSTRATIONS PROJECT

Relativistic Ground State of Hydrogen-Like Atoms

​
Z
1
This Demonstration computes the probability of the upper (red) and lower (gold) components of the ground state of a relativistic hydrogen-like atom of charge
Ze
as a function of
Z
, up to
Z=1/α≈137
, in accordance with the Dirac equation. This is compared to the probability in the standard nonrelativistic theory. The Dirac equation develops a singularity when
Z>1/α
.