DYNAMICAL VARIABLES OF A QUANTUM BARRIER AND WELL UNDER A TIME-DEPENDENT EXTERNAL BIAS - A PATH-INTEGRAL APPROACH

The problem of tunneling of a charged particle through a one-dimension al quantum barrier and formation of stationary states in a well under a time-dependent and a time independent electric bias is exactly solve d using the Feynman path integral method. The coefficients of reflecti on from and transmission through the barrier are dependent on the dura tion of the time for which the external field is applied for both the time-dependent and time-independent biases. A graphical method is desc ribed to find the bound states in a quantum well. The wave-functions o f the system are also calculated.