Eigenstates and spectrum properties of a resonant field in a Kerr-like medium

We investigate the energy eigenvalues and eigenstates of a resonant field in a Kerr-like medium by an efficient method. All the energy eigenvalues and eigenstates can be obtained for an arbitrary total particle number N and other parameters involved in the system. We show that the eigenstates can be explicitly expressed analytically in terms of a single parameter γ whose values are determined by the roots of a polynomial of the order of at most 1 + int(N/2) with int(x) being x's integer part. By studying the spectra, the erratic level crossings appear apparent when N ≥ 40 and γ over critical values