ENERGY EIGENVALUE LEVELS AND SINGULAR POINT ANALYSIS

From the eigenvalue equation H-lambda\PSI-n(lambda) > = E(n) (lambda)\PSI-n(lambda) > where H-lambda = H0 + lambda-V one can derive an autonomous system of first-order differential equations for the eigenvalues E(n)(lambda) and the matrix elements V(mn)(lambda) where lambda is the independent variable. We perform a Painleve test for a three-level system. It turns out that the equations of motion do not pass the Painleve test as such but in a weaker form. We show that the singular point analysis can be extended, since the singular points occur in complex conjugate pairs.