DISPERSION-RELATIONS FOR SURFACE EXCITATIONS AS A PROBE FOR VARIATIONAL SOLUTIONS OF OPTIMIZED PAIRED-PHONON ANALYSIS EQUATIONS

The self-consistency of solutions obtained from a recently proposed numerical relaxation method of solving the Euler-Lagrange equations for the ground state of inhomogeneous Bose systems at zero temperature is investigated. For this kind of system at least three different dispersion relations can be formulated, all of them providing information about the same eigenstates. The quality of our optimization scheme is studied by analyzing the convergence of the low-lying eigenvalues and eigenfunctions of these dispersion relations. Numerical results for the spectrum and spatial shape of elementary excitations of a thin film of liquid He4 supported by an external potential are reported. The optimal lowest-lying eigenvalues are compared with estimations based on simple theoretical approaches and with calculations performed by other authors. © 1990 The American Physical Society.