Eigenstructure of the 1-particle density operator corresponding to the first excited state of two coupled oscillators (Q1075664)

The author investigates the eigenstructure of the 1-particle density operator \(\rho\) corresponding to the first excited state of two 1- dimensional coupled oscillators. It is shown that \(\rho\) is strictly positive, and a Hamiltonian is constructed for which \(\rho\) is the canonical density matrix of the corresponding effective Hamiltonian system. The exact form of the eigenfunctions and their dependence on the eigenvalues is found, some properties of the spectrum are proved, a method for determining a finite number of terms in power expansion of eigenvalues with respect to parameter \(\lambda\in (0,1)\) is given.