Solving 3D TDSE with Runge-Kutta Method

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In summary, the conversation discusses the use of the Runge-Kutta method in 3-D to solve the 3-D TDSE and whether there are any differences compared to the 1-D method. The question also arises about implementation of the spatial part and the importance of boundary conditions. It is concluded that there should be no difference in using the Runge-Kutta method for the time step in 1-D or 3-D, and the wavefunction can be propagated forward in time using finite differences for partial derivatives with respect to spatial coordinates.
  • #1
thatboi
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Hey all,
For the Runge-Kutta method in 3-D (specifically to solve the 3-D TDSE), I was wondering if there were any subtleties I should expect, or if I could just simply use the 1-d method and add on the respective contributions from the other 2 dimensions.
Thanks.
 
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  • #2
I guess you mean applying a Runge-Kutta method for the time step. How do you plan to implement the spatial part?

In principle, there should be no difference between 1D and 3D for the time part.
 
  • #3
DrClaude said:
I guess you mean applying a Runge-Kutta method for the time step. How do you plan to implement the spatial part?

In principle, there should be no difference between 1D and 3D for the time part.
Since I just need to propagate the wavefunction forward in time I figured I could just discretize the space and use finite differences for any partial derivatives with respect to spacial coordinates.
 
  • #4
Sure, but what about boundary conditions?
 
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