  We investigate the Leggett-Garg inequalities and the relative entropy of
coherence in the Bixon-Jortner model. First, we analytically derive the general
solution of the Bixon-Jortner model by a technique of the Laplace transform. So
far, only a special solution has been known for this model. The model has a
single state coupled to equally spaced quasi-continuum states. These couplings
cause discontinuities in the time evolution of the occupation probability of
each state. Second, using the analytical solution, we show that the probability
distribution of the quasi-continuum states approaches the Lorentzian function
in a period of time between the initial time and the first discontinuity.
Third, we examine violation of the Leggett-Garg inequalities and temporal
variation of the relative entropy of coherence in the model. We prove that both
the inequalities and the relative entropy are invariant under transformations
of the energy-level detuning of the single state.
