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- MATLAB
- Thread starter Frank Castle
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In summary, the time-dependent Schrödinger equation can be solved numerically using a finite difference (interpolation) method, but this is less stable and requires smaller step sizes than using an ODE solver such as ode45.f

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Yes, I appreciate that, but if one is solving it for the one-dimensional case it can be treated as an ODE. I was just wondering if in general certain cases are better suited to using ode45 (or other Runge-Kutta like methods), or using interpolation techniques to numerically integrate (using finite difference methods)?!

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Not the time-Yes, I appreciate that, but if one is solving it for the one-dimensional case it can be treated as an ODE.

You can use ODE methods with the TDSE if you express it in terms of a basis set, since you then get a set of coupled ODEs for the basis coefficients.

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Not the time-dependentSchrödinger equation.

You can use ODE methods with the TDSE if you express it in terms of a basis set, since you then get a set of coupled ODEs for the basis coefficients.

Is it more efficient to use a finite difference method to integrate in this case then?

In general, are there cases where it is better to use a finite difference (interpolation) method than using an ODE solver such as ode45?

Is this because the the time dependent Schrödinger equation is a so-called "stiff" equation? Is this why finite difference techniques are preferred over ODE solvers in certain situations, as the latter can be much less stable?

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Unless the number of discrete states of the system is small, grid methods are usually more efficient (fewer grid points are needed than basis functions for a similar problem).In general, are there cases where it is better to use a finite difference (interpolation) method than using an ODE solver such as ode45?

Personally, I prefer the split-operator method, where the kinetic energy operator is dealt with in momentum space, using FFTs.

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Why not use PDEPE?

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Why not use PDEPE?

Is that a PDE solver in matlab?

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