  Energies of quantum states are given by the arguments of phase-evolution
exponentials. It follows then that an analysis of the energies of a two-state
system (TSS) can revolve around phase-emphasized description of states'
probability amplitudes in the Schrodinger picture. Here, studying energies of
TSSs semi-classically, we suggest an energy-revealing format in which the
time-dependence of the probability amplitudes is expressed by phase-evolution
factors only. With this fresh energy-studying approach, we first revisit
non-driven TSSs, write the conditions for setting a system (in general) in a
stationary state, and identify the associated (single) definite energy. Then,
more importantly, we revisit driven-TSSs, identify the two stationary states
and prove the existence of two quasi-energies associated with each stationary
state. Resulting from our phase-keeping framework, we display a
"breathing-spiral" type precession-mode of a strongly-driven spin one-half TSS.
Further, we exemplify our findings through a set of two coupling-probe computer
simulations. For specific examples, we compute and list the energies of several
concrete TSSs under typical operating conditions.
