- Demonstrate that
when
, where
is the momentum operator, and
is a real function of the position operator,
.
Hence, show that the Hamiltonian (870) is Hermitian.
- Find the selection rules for the matrix elements
,
,
and
to be non-zero. Here,
denotes an energy eigenket of a hydrogen-like
atom corresponding to the conventional quantum numbers,
,
, and
.
- Demonstrate that
- Demonstrate that the spontaneous decay rate (via an electric dipole transition) from any 2p state to a 1s state
of a hydrogen atom is

where is the Bohr radius.