
154 Commutation Relations, Normal Ordering, and Stirling Numbers
where a complete account can be found. The calculation determines the (discrete) energy
levels to E
n
= −
me
4
2
2
n
2
, depending only on the principal quantum number n.Comparing
this with (5.5) shows agreement, provided the Rydberg constant is given by R =
me
4
4πc
3
.The
stationary states depend on further quantum numbers, meaning that the energy levels are
degenerated (except for the ground state).
Before we turn in the following subsections to several different aspects of quantum
theory, we would like to mention that an algebraic treatment – Dirac’s quantum algebra
– of the algebra generated