Which of the following is the Green's function for the time-dependent free-particle Schrödinger equation in one dimension?
The time-dependent free-particle Schrödinger equation in one dimension is
Note: Recall that a solution to the time-dependent Schrödinger equation can be written out in a basis of solutions to the time-independent Schrödinger equation
where is the energy of the time-independent eigenfunction .
Notations:
denotes the exponential function, .
denotes the absolute value function.