B. NUMERICAL METHOD. C. COMPARISON OF THE METHODS. IV. CONCLUSIONS. 14 A code based on the Crank-Nicholson algorithm was developed to solve the TBC problem. All of the code was written in the C programming language and the calculations were performed on a LINUX workstation using the GNU compiler. The major effort has gone into adapting the techniques of TBCs because it is complicated by the fact that the boundary condition is non-local in the time, but rather depends on a convolution related to fractional calculus that cannot be treated by standard techniques. The standard algorithm had to be modified to include the non-local, time dependent boundary conditions, which now have to be updated at each time step. To solve the Schrödinger equation on the finite interval, the LU decomposition method was employed. The function libraries were obtained from the open source literature for the GNU compiler. The first set of plots compare the real part of the wave function for both methods at the same time steps t = 0 . 1 , t = 0 . 2 , and t = 1 . 4 as shown in figures 2 and 3. The second set of plots, figures 4 and 5, compare the imaginary part of the wave function for both methods at the same time steps t = 0 . 01 , t = 0 . 1 , and t = 1 . 4 . The comparison between the plots for each method shows an excellent agreement as we expected. This confirms the adequate implementation of the numerical method for a QIVP. Therefore, the basis can be established for a more complex version of the RTBC . In this work we investigated the problem of solving the time dependent Schrodinger equation within a confined region when a constraint is suddenly removed. We accomplished two important goals; the first one is of physical significance. We determined the wave function at any time t, and therefore provided all the physical information for the evolution of the EP within the trap. Therefore, we are able to extract important physical properties of the system such as the mean fraction of mass inside the region, which is called the survival probability, as well as the time dependence of the properties of the particle kinetic energy, potential energy, the total energy, etc.. Since it is assumed that the particle density in the