Solving 3D TDSE with Runge-Kutta Method

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Discussion Overview

The discussion centers around the application of the Runge-Kutta method to solve the three-dimensional time-dependent Schrödinger equation (TDSE). Participants explore the nuances of extending the method from one dimension to three dimensions, particularly focusing on time-stepping and spatial implementation.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about potential subtleties when applying the Runge-Kutta method in 3D compared to 1D.
  • Another participant suggests that there should be no difference in the time-stepping aspect between 1D and 3D.
  • A further contribution mentions the intention to use finite differences for spatial derivatives while propagating the wavefunction in time.
  • A later reply raises a question regarding the handling of boundary conditions in this context.

Areas of Agreement / Disagreement

Participants generally agree that the time-stepping aspect of the Runge-Kutta method does not differ between dimensions, but there are unresolved questions regarding the spatial implementation and boundary conditions.

Contextual Notes

Limitations include the lack of detail on specific boundary conditions and how they might affect the implementation of the method in three dimensions.

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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