IN THIS PAPER WE GIVE THE TIME DEPENDENT DESCRIPTION OF THE SCATTERING OF A WAVE PACKET BY A SHORT RANGE POTENTIAL. WE SHOW THAT WHEN THE WAVE PACKET IS INITIALLY OUTSIDE THE SCATTERER, IT IS POSIBLE TO INTRODUCE AN APPROPIATE TIME DEPENDENT GREEN FUNCTION TO DESCRIBE THE SCATTERING PROCESS. THIS GREEN FUNCTION WILL BE EVALUATED EXPLICITLY IN TERM OF ERROR INTEGRAL FUNCTIONS, AND THE ONLY PARAMETERS THAT APPEAR IN THE GREEN FUNCTION WILL BE THE POLES OF THE S MATRIX. FROM THE ASYMPTOTIC BEHAVIOR OF THE GREEN FUNCTIOR WHEN T, WE OBTAIN RESTRICIONS ON THE POSITION OF THE POLES OF THE S MATRIX WHICH AGREE WITH THOSE DUE TO THE DEFINITION OF THE S IN TERMS OF THE DERIVATIVE MATRIX R. THE PRESENT ANALYSIS IS CARRIED OUT FOR ARBITRARY ANGULAR MOMENTUM.IN THIS PAPER WE GIVE THE TIME DEPENDENT DESCRIPTION OF THE SCATTERING OF A WAVE PACKET BY A SHORT RANGE POTENTIAL. WE SHOW THAT WHEN THE WAVE PACKET IS INITIALLY OUTSIDE THE SCATTERER, IT IS POSIBLE TO INTRODUCE AN APPROPIATE TIME DEPENDENT GREEN FUNCTION TO DESCRIBE THE SCATTERING PROCESS. THIS GREEN FUNCTION WILL BE EVALUATED EXPLICITLY IN TERM OF ERROR INTEGRAL FUNCTIONS, AND THE ONLY PARAMETERS THAT APPEAR IN THE GREEN FUNCTION WILL BE THE POLES OF THE S MATRIX. FROM THE ASYMPTOTIC BEHAVIOR OF THE GREEN FUNCTIOR WHEN T, WE OBTAIN RESTRICIONS ON THE POSITION OF THE POLES OF THE S MATRIX WHICH AGREE WITH THOSE DUE TO THE DEFINITION OF THE S IN TERMS OF THE DERIVATIVE MATRIX R. THE PRESENT ANALYSIS IS CARRIED OUT FOR ARBITRARY ANGULAR MOMENTUM.