Iterative Solutions for Low Lying Excited States of a Class of   Schroedinger Equation
  The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling $g$ is not too small. 
R. Friedberg, T. D. Lee and W. Q. Zhao