ABSTRACT
Figure 2.1 shows a schematic diagram of a two-level system, called
a two-level atom, with the ground state |1〉 and the upper (excited) state |2〉. In fact, the electron can make transitions between many energy states, but we can limit the transitions to only between two
states. In practice, it is done by a suitable choice of the frequency of
an external field that will force the electron to oscillate only between
these two selected states [3, 4]. Multi-level transitions involving
more than two energy states are much more complex and we are
not intend to consider them here, but the formalism presented here
can be extended to multi-level cases.a
The energy of the electron in the selected states |2〉 and |1〉 is determined by the stationary Schro¨dinger equation
HˆA |1〉 = E1 |1〉 , HˆA |2〉 = E2 |2〉 , (2.10) where HˆA is the Hamiltonian of the atom whose explicit form is to be determine.
