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jimmy neutron
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Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?
It is for the time independent Schrodinger Equation and for ground state solutionsoarce said:It is time dependent SE or stationay SE? If it is stationary you need the ground solution or some excited state solution?
Periodic boundary conditions are a set of mathematical rules used to model how a system behaves when it is constrained within a finite space. In this context, the boundaries of the space are considered to be periodic, meaning that they are connected in a way that allows for the system to repeat itself periodically.
In numerical solutions, periodic boundary conditions are typically applied by imposing restrictions on the values of the solution at the boundaries of the computational domain. These restrictions ensure that the solution remains periodic, even when the boundaries are reached.
One advantage of using periodic boundary conditions is that they allow for the simulation of systems with large spatial extents, without the need for an extremely large computational domain. Additionally, periodic boundary conditions can help to reduce the effects of boundary conditions on the solution, making it more accurate.
Periodic boundary conditions are not suitable for all systems and may not accurately represent the behavior of some physical systems. In particular, they may not be appropriate for systems with strong gradients or discontinuities near the boundaries.
The appropriateness of using periodic boundary conditions can be determined by analyzing the behavior of the system near the boundaries and considering the specific physical properties of the system. It may also be helpful to compare the results obtained with and without periodic boundary conditions to assess their impact on the solution.