Solving 3D TDSE with Runge-Kutta Method

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SUMMARY

The discussion focuses on applying the Runge-Kutta method to solve the 3-D Time-Dependent Schrödinger Equation (TDSE). Participants confirm that the time-stepping process remains consistent between 1D and 3D implementations. The conversation highlights the necessity of discretizing spatial dimensions and using finite differences for spatial derivatives. Additionally, the importance of addressing boundary conditions in the spatial implementation is emphasized.

PREREQUISITES
  • Understanding of the Time-Dependent Schrödinger Equation (TDSE)
  • Familiarity with the Runge-Kutta method for numerical integration
  • Knowledge of finite difference methods for spatial discretization
  • Concepts of boundary conditions in differential equations
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  • Research the implementation of the Runge-Kutta method in 3D simulations
  • Study finite difference techniques for solving partial differential equations
  • Explore boundary condition types and their applications in quantum mechanics
  • Learn about numerical stability and convergence in time-stepping methods
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Physicists, computational scientists, and researchers working on quantum mechanics simulations, particularly those interested in numerical methods for solving the Time-Dependent Schrödinger Equation.

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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