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Numerically solutions with periodic boundary conditions

  1. Sep 22, 2014 #1
    Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?
  2. jcsd
  3. Sep 23, 2014 #2
    It is time dependent SE or stationay SE? If it is stationary you need the ground solution or some excited state solution?
  4. Sep 24, 2014 #3
    It is for the time independent Schrodinger Equation and for ground state solution
  5. Sep 24, 2014 #4
    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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