Undergrad Solving 3D TDSE with Runge-Kutta Method

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The discussion focuses on using the Runge-Kutta method to solve the 3D Time-Dependent Schrödinger Equation (TDSE). Participants agree that the time-stepping aspect of the Runge-Kutta method should not differ between 1D and 3D implementations. The main concern raised is how to effectively handle the spatial components, suggesting the use of finite differences for spatial derivatives. Additionally, the importance of considering boundary conditions in the implementation is highlighted. Overall, the conversation emphasizes the need for careful spatial discretization and boundary condition management in 3D TDSE solutions.
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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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.
 
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.
 
Sure, but what about boundary conditions?
 

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