Abstract: The one-dimensional quantum bound-state solution of the initial value problem is studied. A lemma and an associated inference are derived, as well as a rational formula for choosing initial conditions in the classically forbidden area is obtained. The ＂shooting method＂ is used to determine the energy of eigenvalues and eigenfun- tions. The method is simple and intuitive, and can be extended to solve the radial wave function in the multidimen- sional space.

Key words: quantum bound states, initial value solution, shooting method