Numerically solutions with periodic boundary conditions

  • #1
Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?
 

Answers and Replies

  • #2
155
24
It is time dependent SE or stationay SE? If it is stationary you need the ground solution or some excited state solution?
 
  • #3
It is time dependent SE or stationay SE? If it is stationary you need the ground solution or some excited state solution?
It is for the time independent Schrodinger Equation and for ground state solution
 
  • #4
155
24
For time dependent equation I would start by split-step method, when using Fourier Transform you get by default the periodic boundary conditions: http://en.wikipedia.org/wiki/Split-step_method otherwise you would need to implement a propagation method (Euler, Crank-Nicholson etc).
As for stationary solutions you can you the symmetry of your solution, i.e. translation invariant, to rewrite your solution on a closed interval [a,b] and the use, for instance, shooting method http://en.wikipedia.org/wiki/Shooting_method
 

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