  The Feynman all-coupling variational approach for the polaron is
re-formulated and extended using the Hamiltonian formalism with time-ordered
operator calculus. Special attention is devoted to the excited polaron states.
The energy levels and the inverse lifetimes of the excited polaron states are,
for the first time, explicitly derived within this all-coupling approach.
Remarkable agreement of the obtained transition energies with the peak
positions of the polaron optical conductivity calculated using diagrammatic
quantum Monte Carlo is obtained.
